diff --git a/doc/api/next_api_changes/2019-01-04-SH.rst b/doc/api/next_api_changes/2019-01-04-SH.rst
new file mode 100644
index 000000000000..147b7009c36d
--- /dev/null
+++ b/doc/api/next_api_changes/2019-01-04-SH.rst
@@ -0,0 +1,13 @@
+Changes to ``twin*`` methods in `mpl_toolkits.axes_grid1`
+-----------------------------------------------------------
+
+Previously, calling `~mpl_toolkits.axes_grid1.parasite_axes.HostAxesBase.twin`,
+`~mpl_toolkits.axes_grid1.parasite_axes.HostAxesBase.twinx` or
+`~mpl_toolkits.axes_grid1.parasite_axes.HostAxesBase.twiny` on
+`mpl_toolkits.axes_grid1` host axes would hide the host axes' own axis
+lines so that there is no overdrawing with the twin/parasite axes' axis lines.
+This could lead to surprising behavior in certain cases
+(`#10748 <https://github.com/matplotlib/matplotlib/issues/10748>`_), so the
+logic has now been reversed, such that host axis lines are kept visible and
+twin/parasite axis lines are hidden. This may break code which relies on the
+specifics of host/parasite axis line visibility.
diff --git a/lib/mpl_toolkits/axes_grid1/parasite_axes.py b/lib/mpl_toolkits/axes_grid1/parasite_axes.py
index 900dac19a8b1..d1b27974af59 100644
--- a/lib/mpl_toolkits/axes_grid1/parasite_axes.py
+++ b/lib/mpl_toolkits/axes_grid1/parasite_axes.py
@@ -249,17 +249,15 @@ def twinx(self, axes_class=None):
         self.parasites.append(ax2)
         ax2._remove_method = self._remove_twinx
 
-        self.axis["right"].set_visible(False)
-
         ax2.axis["right"].set_visible(True)
+        ax2.axis["right"].toggle(all=True)
+        ax2.axis["right"].line.set_visible(False)
         ax2.axis["left", "top", "bottom"].set_visible(False)
 
         return ax2
 
     def _remove_twinx(self, ax):
         self.parasites.remove(ax)
-        self.axis["right"].set_visible(True)
-        self.axis["right"].toggle(ticklabels=False, label=False)
 
     def twiny(self, axes_class=None):
         """
@@ -278,17 +276,15 @@ def twiny(self, axes_class=None):
         self.parasites.append(ax2)
         ax2._remove_method = self._remove_twiny
 
-        self.axis["top"].set_visible(False)
-
         ax2.axis["top"].set_visible(True)
+        ax2.axis["top"].toggle(all=True)
+        ax2.axis["top"].line.set_visible(False)
         ax2.axis["left", "right", "bottom"].set_visible(False)
 
         return ax2
 
     def _remove_twiny(self, ax):
         self.parasites.remove(ax)
-        self.axis["top"].set_visible(True)
-        self.axis["top"].toggle(ticklabels=False, label=False)
 
     def twin(self, aux_trans=None, axes_class=None):
         """
@@ -313,15 +309,13 @@ def twin(self, aux_trans=None, axes_class=None):
         self.parasites.append(ax2)
         ax2._remove_method = self.parasites.remove
 
-        self.axis["top", "right"].set_visible(False)
-
         ax2.axis["top", "right"].set_visible(True)
+        ax2.axis["top", "right"].toggle(all=True)
+        ax2.axis["top", "right"].line.set_visible(False)
         ax2.axis["left", "bottom"].set_visible(False)
 
         def _remove_method(h):
             self.parasites.remove(h)
-            self.axis["top", "right"].set_visible(True)
-            self.axis["top", "right"].toggle(ticklabels=False, label=False)
         ax2._remove_method = _remove_method
 
         return ax2
diff --git a/lib/mpl_toolkits/tests/baseline_images/test_axes_grid1/twin_axes_empty_and_removed.png b/lib/mpl_toolkits/tests/baseline_images/test_axes_grid1/twin_axes_empty_and_removed.png
index 096104fa0533..7dce51c7bef7 100644
Binary files a/lib/mpl_toolkits/tests/baseline_images/test_axes_grid1/twin_axes_empty_and_removed.png and b/lib/mpl_toolkits/tests/baseline_images/test_axes_grid1/twin_axes_empty_and_removed.png differ