diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index f9aaafc66ddc..7ceea3430bf5 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -1477,11 +1477,21 @@ def update_units(self, data):
             self.set_units(default)
 
         if neednew:
-            self._update_axisinfo()
+            if np.iterable(data):
+                try:
+                    data_interval = (np.min(data), np.max(data))
+                except (TypeError, ValueError):
+                    data_interval = None
+                else:
+                    if data_interval[0] == data_interval[1]:
+                        data_interval = None
+            else:
+                data_interval = None
+            self._update_axisinfo(data_interval)
         self.stale = True
         return True
 
-    def _update_axisinfo(self):
+    def _update_axisinfo(self, data_interval=None):
         """
         Check the axis converter for the stored units to see if the
         axis info needs to be updated.
@@ -1513,7 +1523,7 @@ def _update_axisinfo(self):
             self.set_label_text(info.label)
             self.isDefault_label = True
 
-        self.set_default_intervals()
+        self.set_default_intervals(data_interval)
 
     def have_units(self):
         return self.converter is not None or self.units is not None
@@ -2277,15 +2287,18 @@ def set_inverted(self, inverted):
         # cast to bool to avoid bad interaction between python 3.8 and np.bool_
         self.axes.set_xlim(sorted((a, b), reverse=bool(inverted)), auto=None)
 
-    def set_default_intervals(self):
+    def set_default_intervals(self, data_interval=None):
         # docstring inherited
-        xmin, xmax = 0., 1.
+        xmin, xmax = (0., 1.) if data_interval is None else data_interval
         dataMutated = self.axes.dataLim.mutatedx()
         viewMutated = self.axes.viewLim.mutatedx()
         if not dataMutated or not viewMutated:
             if self.converter is not None:
                 info = self.converter.axisinfo(self.units, self)
-                if info.default_limits is not None:
+                if data_interval is not None:
+                    xmin = self.converter.convert(xmin, self.units, self)
+                    xmax = self.converter.convert(xmax, self.units, self)
+                elif info.default_limits is not None:
                     valmin, valmax = info.default_limits
                     xmin = self.converter.convert(valmin, self.units, self)
                     xmax = self.converter.convert(valmax, self.units, self)
@@ -2561,15 +2574,18 @@ def set_inverted(self, inverted):
         # cast to bool to avoid bad interaction between python 3.8 and np.bool_
         self.axes.set_ylim(sorted((a, b), reverse=bool(inverted)), auto=None)
 
-    def set_default_intervals(self):
+    def set_default_intervals(self, data_interval=None):
         # docstring inherited
-        ymin, ymax = 0., 1.
+        ymin, ymax = (0., 1.) if data_interval is None else data_interval
         dataMutated = self.axes.dataLim.mutatedy()
         viewMutated = self.axes.viewLim.mutatedy()
         if not dataMutated or not viewMutated:
             if self.converter is not None:
                 info = self.converter.axisinfo(self.units, self)
-                if info.default_limits is not None:
+                if data_interval is not None:
+                    ymin = self.converter.convert(ymin, self.units, self)
+                    ymax = self.converter.convert(ymax, self.units, self)
+                elif info.default_limits is not None:
                     valmin, valmax = info.default_limits
                     ymin = self.converter.convert(valmin, self.units, self)
                     ymax = self.converter.convert(valmax, self.units, self)
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 4a877f0b9642..c49a13b1d8cd 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -6824,3 +6824,46 @@ def test_ylabel_ha_with_position(ha):
     ax.set_ylabel("test", y=1, ha=ha)
     ax.yaxis.set_label_position("right")
     assert ax.yaxis.get_label().get_ha() == ha
+
+
+def test_axhline_with_date_xaxis():
+    fig, ax = plt.subplots()
+    ax.axhline(1.5)
+    x = [datetime.datetime(2020, 1, i) for i in range(1, 3)]
+    y = [1, 2]
+    ax.plot(x, y)
+    assert ax.get_xlim() == (18262.0, 18263.0)
+
+
+def test_axvline_with_date_yaxis():
+    fig, ax = plt.subplots()
+    ax.axvline(1.5)
+    x = [1, 2]
+    y = [datetime.datetime(2020, 1, i) for i in range(1, 3)]
+    ax.plot(x, y)
+    assert ax.get_ylim() == (18262.0, 18263.0)
+
+
+def test_two_spans():
+    fig, ax = plt.subplots()
+    ax.axhline(1)
+    ax.axhline(2)
+    assert ax.get_ylim() == (1.0, 2.0)
+
+
+def test_axhspan_with_date_xaxis():
+    fig, ax = plt.subplots()
+    ax.axhspan(1, 2)
+    x = [datetime.datetime(2020, 1, i) for i in range(1, 3)]
+    y = [1, 2]
+    ax.plot(x, y)
+    assert ax.get_xlim() == (18262.0, 18263.0)
+
+
+def test_axvspan_with_date_yaxis():
+    fig, ax = plt.subplots()
+    ax.axvspan(1, 2)
+    x = [1, 2]
+    y = [datetime.datetime(2020, 1, i) for i in range(1, 3)]
+    ax.plot(x, y)
+    assert ax.get_ylim() == (18262.0, 18263.0)