diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index ed5275333fda1..32a66be8b3b75 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -712,6 +712,7 @@ Reshaping
 - Fixed metadata propagation in :meth:`Dataframe.apply` method, consequently fixing the same issue for :meth:`Dataframe.transform`, :meth:`Dataframe.nunique` and :meth:`Dataframe.mode` (:issue:`28283`)
 - Bug in :meth:`DataFrame.stack` with ``ExtensionDtype`` columns incorrectly raising (:issue:`43561`)
 - Bug in :meth:`Series.unstack` with object doing unwanted type inference on resulting columns (:issue:`44595`)
+- Bug in :class:`MultiIndex` failing join operations with overlapping ``IntervalIndex`` levels (:issue:`44096`)
 -
 
 Sparse
diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index 92837a43e2b69..670034c4dc4c1 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -649,7 +649,7 @@ cdef class BaseMultiIndexCodesEngine:
             Integers representing one combination each
         """
         zt = [target._get_level_values(i) for i in range(target.nlevels)]
-        level_codes = [lev.get_indexer(codes) + 1 for lev, codes
+        level_codes = [lev.get_indexer_for(codes) + 1 for lev, codes
                        in zip(self.levels, zt)]
         return self._codes_to_ints(np.array(level_codes, dtype='uint64').T)
 
diff --git a/pandas/tests/indexes/multi/test_join.py b/pandas/tests/indexes/multi/test_join.py
index 3aa0ac1676acc..e6bec97aedb38 100644
--- a/pandas/tests/indexes/multi/test_join.py
+++ b/pandas/tests/indexes/multi/test_join.py
@@ -3,6 +3,7 @@
 
 from pandas import (
     Index,
+    Interval,
     MultiIndex,
 )
 import pandas._testing as tm
@@ -115,3 +116,45 @@ def test_join_multi_return_indexers():
 
     result = midx1.join(midx2, return_indexers=False)
     tm.assert_index_equal(result, midx1)
+
+
+def test_join_overlapping_interval_level():
+    # GH 44096
+    idx_1 = MultiIndex.from_tuples(
+        [
+            (1, Interval(0.0, 1.0)),
+            (1, Interval(1.0, 2.0)),
+            (1, Interval(2.0, 5.0)),
+            (2, Interval(0.0, 1.0)),
+            (2, Interval(1.0, 3.0)),  # interval limit is here at 3.0, not at 2.0
+            (2, Interval(3.0, 5.0)),
+        ],
+        names=["num", "interval"],
+    )
+
+    idx_2 = MultiIndex.from_tuples(
+        [
+            (1, Interval(2.0, 5.0)),
+            (1, Interval(0.0, 1.0)),
+            (1, Interval(1.0, 2.0)),
+            (2, Interval(3.0, 5.0)),
+            (2, Interval(0.0, 1.0)),
+            (2, Interval(1.0, 3.0)),
+        ],
+        names=["num", "interval"],
+    )
+
+    expected = MultiIndex.from_tuples(
+        [
+            (1, Interval(0.0, 1.0)),
+            (1, Interval(1.0, 2.0)),
+            (1, Interval(2.0, 5.0)),
+            (2, Interval(0.0, 1.0)),
+            (2, Interval(1.0, 3.0)),
+            (2, Interval(3.0, 5.0)),
+        ],
+        names=["num", "interval"],
+    )
+    result = idx_1.join(idx_2, how="outer")
+
+    tm.assert_index_equal(result, expected)