diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index a667d0663aa31..0d3a9a8f969a4 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -401,6 +401,7 @@ Other
 - Bug in :meth:`DataFrame.to_records` incorrectly losing timezone information in timezone-aware ``datetime64`` columns (:issue:`32535`)
 - Fixed :func:`pandas.testing.assert_series_equal` to correctly raise if left object is a different subclass with ``check_series_type=True`` (:issue:`32670`).
 - :meth:`IntegerArray.astype` now supports ``datetime64`` dtype (:issue:32538`)
+- Fixed bug in :func:`pandas.testing.assert_series_equal` where dtypes were checked for ``Interval`` and ``ExtensionArray`` operands when ``check_dtype`` was ``False`` (:issue:`32747`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/_testing.py b/pandas/_testing.py
index d473b453d77d2..f96e3872eb8bd 100644
--- a/pandas/_testing.py
+++ b/pandas/_testing.py
@@ -1160,7 +1160,7 @@ def assert_series_equal(
                 f"is not equal to {right._values}."
             )
             raise AssertionError(msg)
-    elif is_interval_dtype(left.dtype) or is_interval_dtype(right.dtype):
+    elif is_interval_dtype(left.dtype) and is_interval_dtype(right.dtype):
         assert_interval_array_equal(left.array, right.array)
     elif is_categorical_dtype(left.dtype) or is_categorical_dtype(right.dtype):
         _testing.assert_almost_equal(
@@ -1170,7 +1170,7 @@ def assert_series_equal(
             check_dtype=check_dtype,
             obj=str(obj),
         )
-    elif is_extension_array_dtype(left.dtype) or is_extension_array_dtype(right.dtype):
+    elif is_extension_array_dtype(left.dtype) and is_extension_array_dtype(right.dtype):
         assert_extension_array_equal(left._values, right._values)
     elif needs_i8_conversion(left.dtype) or needs_i8_conversion(right.dtype):
         # DatetimeArray or TimedeltaArray
diff --git a/pandas/tests/util/test_assert_frame_equal.py b/pandas/tests/util/test_assert_frame_equal.py
index 3090343ba2fd9..4bcf7087c239d 100644
--- a/pandas/tests/util/test_assert_frame_equal.py
+++ b/pandas/tests/util/test_assert_frame_equal.py
@@ -1,5 +1,6 @@
 import pytest
 
+import pandas as pd
 from pandas import DataFrame
 import pandas._testing as tm
 
@@ -218,3 +219,41 @@ def test_frame_equal_unicode(df1, df2, msg, by_blocks_fixture, obj_fixture):
     msg = msg.format(obj=obj_fixture)
     with pytest.raises(AssertionError, match=msg):
         tm.assert_frame_equal(df1, df2, by_blocks=by_blocks_fixture, obj=obj_fixture)
+
+
+def test_assert_frame_equal_extension_dtype_mismatch():
+    # https://github.com/pandas-dev/pandas/issues/32747
+    left = DataFrame({"a": [1, 2, 3]}, dtype="Int64")
+    right = left.astype(int)
+
+    msg = (
+        "Attributes of DataFrame\\.iloc\\[:, 0\\] "
+        '\\(column name="a"\\) are different\n\n'
+        'Attribute "dtype" are different\n'
+        "\\[left\\]:  Int64\n"
+        "\\[right\\]: int[32|64]"
+    )
+
+    tm.assert_frame_equal(left, right, check_dtype=False)
+
+    with pytest.raises(AssertionError, match=msg):
+        tm.assert_frame_equal(left, right, check_dtype=True)
+
+
+def test_assert_frame_equal_interval_dtype_mismatch():
+    # https://github.com/pandas-dev/pandas/issues/32747
+    left = DataFrame({"a": [pd.Interval(0, 1)]}, dtype="interval")
+    right = left.astype(object)
+
+    msg = (
+        "Attributes of DataFrame\\.iloc\\[:, 0\\] "
+        '\\(column name="a"\\) are different\n\n'
+        'Attribute "dtype" are different\n'
+        "\\[left\\]:  interval\\[int64\\]\n"
+        "\\[right\\]: object"
+    )
+
+    tm.assert_frame_equal(left, right, check_dtype=False)
+
+    with pytest.raises(AssertionError, match=msg):
+        tm.assert_frame_equal(left, right, check_dtype=True)
diff --git a/pandas/tests/util/test_assert_series_equal.py b/pandas/tests/util/test_assert_series_equal.py
index 2550b32446055..49f5489a2e2f1 100644
--- a/pandas/tests/util/test_assert_series_equal.py
+++ b/pandas/tests/util/test_assert_series_equal.py
@@ -1,5 +1,6 @@
 import pytest
 
+import pandas as pd
 from pandas import Categorical, DataFrame, Series
 import pandas._testing as tm
 
@@ -196,6 +197,40 @@ def test_series_equal_categorical_mismatch(check_categorical):
         _assert_series_equal_both(s1, s2, check_categorical=check_categorical)
 
 
+def test_assert_series_equal_extension_dtype_mismatch():
+    # https://github.com/pandas-dev/pandas/issues/32747
+    left = Series(pd.array([1, 2, 3], dtype="Int64"))
+    right = left.astype(int)
+
+    msg = """Attributes of Series are different
+
+Attribute "dtype" are different
+\\[left\\]:  Int64
+\\[right\\]: int[32|64]"""
+
+    tm.assert_series_equal(left, right, check_dtype=False)
+
+    with pytest.raises(AssertionError, match=msg):
+        tm.assert_series_equal(left, right, check_dtype=True)
+
+
+def test_assert_series_equal_interval_dtype_mismatch():
+    # https://github.com/pandas-dev/pandas/issues/32747
+    left = Series([pd.Interval(0, 1)], dtype="interval")
+    right = left.astype(object)
+
+    msg = """Attributes of Series are different
+
+Attribute "dtype" are different
+\\[left\\]:  interval\\[int64\\]
+\\[right\\]: object"""
+
+    tm.assert_series_equal(left, right, check_dtype=False)
+
+    with pytest.raises(AssertionError, match=msg):
+        tm.assert_series_equal(left, right, check_dtype=True)
+
+
 def test_series_equal_series_type():
     class MySeries(Series):
         pass