diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 7dd7a92b0d3e5c..f50cd2b96c14a4 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -1000,6 +1000,7 @@ Datetimelike
 - Bug in :func:`to_datetime` with an :class:`Index` argument that would drop the ``name`` from the result (:issue:`21697`)
 - Bug in :class:`PeriodIndex` where adding or subtracting a :class:`timedelta` or :class:`Tick` object produced incorrect results (:issue:`22988`)
 - Bug in :func:`date_range` when decrementing a start date to a past end date by a negative frequency (:issue:`23270`)
+- Bug in :func:`DataFrame.combine` with datetimelike values raising a TypeError (:issue:`23079`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 6dd9174028f183..4371fa0379c286 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -5141,22 +5141,14 @@ def combine(self, other, func, fill_value=None, overwrite=True):
                 if not is_dtype_equal(other_dtype, new_dtype):
                     otherSeries = otherSeries.astype(new_dtype)
 
-            # see if we need to be represented as i8 (datetimelike)
-            # try to keep us at this dtype
-            needs_i8_conversion_i = needs_i8_conversion(new_dtype)
-            if needs_i8_conversion_i:
-                arr = func(series, otherSeries, True)
-            else:
-                arr = func(series, otherSeries)
-
+            arr = func(series, otherSeries)
             arr = maybe_downcast_to_dtype(arr, this_dtype)
 
             result[col] = arr
 
         # convert_objects just in case
         return self._constructor(result, index=new_index,
-                                 columns=new_columns)._convert(datetime=True,
-                                                               copy=False)
+                                 columns=new_columns)
 
     def combine_first(self, other):
         """
@@ -5203,15 +5195,27 @@ def combine_first(self, other):
         """
         import pandas.core.computation.expressions as expressions
 
-        def combiner(x, y, needs_i8_conversion=False):
-            x_values = x.values if hasattr(x, 'values') else x
-            y_values = y.values if hasattr(y, 'values') else y
-            if needs_i8_conversion:
-                mask = isna(x)
-                x_values = x_values.view('i8')
-                y_values = y_values.view('i8')
-            else:
-                mask = isna(x_values)
+        def extract_values(arr):
+            # Does two things
+            # maybe gets the values from the Series / Index
+            # convert datelike to i8
+            if isinstance(arr, (ABCIndexClass, ABCSeries)):
+                arr = arr._values
+
+            if needs_i8_conversion(arr):
+                if is_extension_array_dtype(arr.dtype):
+                    arr = arr.asi8
+                else:
+                    arr = arr.view('i8')
+            return arr
+
+        def combiner(x, y):
+            mask = isna(x)
+            if isinstance(mask, (ABCIndexClass, ABCSeries)):
+                mask = mask.values
+
+            x_values = extract_values(x)
+            y_values = extract_values(y)
 
             # If the column y in other DataFrame is not in first DataFrame,
             # just return y_values.
diff --git a/pandas/tests/frame/test_combine_concat.py b/pandas/tests/frame/test_combine_concat.py
index ece9559313ba07..2c0fbe9d585cb2 100644
--- a/pandas/tests/frame/test_combine_concat.py
+++ b/pandas/tests/frame/test_combine_concat.py
@@ -31,6 +31,24 @@ def test_concat_multiple_frames_dtypes(self):
         expected = Series(dict(float64=2, float32=2))
         assert_series_equal(results, expected)
 
+    @pytest.mark.parametrize('data', [
+        pd.date_range('2000', periods=4),
+        pd.date_range('2000', periods=4, tz="US/Central"),
+        pd.period_range('2000', periods=4),
+        pd.timedelta_range(0, periods=4),
+    ])
+    def test_combine_datetlike_udf(self, data):
+        # https://github.com/pandas-dev/pandas/issues/23079
+        df = pd.DataFrame({"A": data})
+        other = df.copy()
+        df.iloc[1, 0] = None
+
+        def combiner(a, b):
+            return b
+
+        result = df.combine(other, combiner)
+        tm.assert_frame_equal(result, other)
+
     def test_concat_multiple_tzs(self):
         # GH 12467
         # combining datetime tz-aware and naive DataFrames