Can you catch a native exception in C# code?

You can use Win32Exception and use its NativeErrorCode property to handle it appropriately.

// http://support.microsoft.com/kb/186550
const int ERROR_FILE_NOT_FOUND = 2;
const int ERROR_ACCESS_DENIED = 5;
const int ERROR_NO_APP_ASSOCIATED = 1155; 

void OpenFile(string filePath)
{
    Process process = new Process();

    try
    {
        // Calls native application registered for the file type
        // This may throw native exception
        process.StartInfo.FileName = filePath;
        process.StartInfo.Verb = "Open";
        process.StartInfo.CreateNoWindow = true;
        process.Start();
    }
    catch (Win32Exception e)
    {
        if (e.NativeErrorCode == ERROR_FILE_NOT_FOUND || 
            e.NativeErrorCode == ERROR_ACCESS_DENIED ||
            e.NativeErrorCode == ERROR_NO_APP_ASSOCIATED)
        {
            MessageBox.Show(this, e.Message, "Error", 
                    MessageBoxButtons.OK, 
                    MessageBoxIcon.Exclamation);
        }
    }
}

Catch without () will catch non-CLS compliant exceptions including native exceptions.

try
{

}
catch
{

}

See the following FxCop rule for more info http://msdn.microsoft.com/en-gb/bb264489.aspx