If your partner's ex doesn't know about you, what do you not know about your partner's ex? Something smells fishy.
I'm so sorry that this is happening to you. If they really are "just friends," why would your partner be afraid to hurt her feelings by telling her she is dating someone? That doesn't make sense to me. It just sounds like your partner doesn't really know who or what she wants. Or she wants both, and is getting both. Does that sound like the healthy kind of partner you want to be with?
Never be anyones "secret"....
I was going to say "no" until I read the bit about your partner keeping you secret from the ex. THAT sounds out of line to me.