Gender-neutral term for a Senator or Representative

Is there a gender-neutral term for a Senator or Representative?

• Senator: gender-neutral, but only includes Senators
• Representative: gender-neutral, but only includes Representatives
• Congressman: male-only, seems to be mostly used for Representatives
• Congresswoman: female-only, seems to be mostly used for Representatives
• Congressperson: gender-neutral, same problem as Congressman and Congresswoman
• Member of Congress: makes the most sense to me, but I've never heard it before