diff --git a/extensions/positron-python/python_files/positron/positron_ipykernel/tests/test_ui.py b/extensions/positron-python/python_files/positron/positron_ipykernel/tests/test_ui.py
index 132da3704f7..bf02f5d0c60 100644
--- a/extensions/positron-python/python_files/positron/positron_ipykernel/tests/test_ui.py
+++ b/extensions/positron-python/python_files/positron/positron_ipykernel/tests/test_ui.py
@@ -278,3 +278,31 @@ def test_plotly_show_sends_events(
     assert params["title"] == ""
     assert params["is_plot"]
     assert params["height"] == 0
+
+
+def test_is_not_plot_url_events(
+    shell: PositronShell,
+    ui_comm: DummyComm,
+) -> None:
+    """
+    Test that opening a URL that is not a plot sends the expected UI events.
+    Checks that the `is_plot` parameter is not sent or is `False`.
+    """
+    shell.run_cell(
+        """\
+import webbrowser
+# Only enable the positron viewer browser; avoids system browsers opening during tests.
+webbrowser._tryorder = ["positron_viewer"]
+
+webbrowser.open("http://127.0.0.1:8000")
+webbrowser.open("file://file.html")
+"""
+    )
+    assert len(ui_comm.messages) == 2
+    params = ui_comm.messages[0]["data"]["params"]
+    assert params["url"] == "http://127.0.0.1:8000"
+    assert "is_plot" not in params
+
+    params = ui_comm.messages[1]["data"]["params"]
+    assert params["path"] == "file.html" if sys.platform == "win32" else "file://file.html"
+    assert params["is_plot"] is False
diff --git a/extensions/positron-python/python_files/positron/positron_ipykernel/ui.py b/extensions/positron-python/python_files/positron/positron_ipykernel/ui.py
index 24fd6ee232b..577a92183e3 100644
--- a/extensions/positron-python/python_files/positron/positron_ipykernel/ui.py
+++ b/extensions/positron-python/python_files/positron/positron_ipykernel/ui.py
@@ -210,18 +210,19 @@ def open(self, url, new=0, autoraise=True) -> bool:
         return False
 
     @staticmethod
-    def _is_module_function(module_name: str, function_name: str = None) -> bool:
+    def _is_module_function(module_name: str, function_name: Union[str, None] = None) -> bool:
         module = sys.modules.get(module_name)
         if module:
-            if function_name:
-                for frame_info in inspect.stack():
+            for frame_info in inspect.stack():
+                if function_name:
                     if (
                         inspect.getmodule(frame_info.frame, frame_info.filename) == module
                         and frame_info.function == function_name
                     ):
                         return True
-            else:
-                return True
+                else:
+                    if inspect.getmodule(frame_info.frame) == module:
+                        return True
         return False
 
     def _send_show_html_event(self, url: str, is_plot: bool) -> bool: