Do you know what your current cadence is?

Yes; you might have to work on your cadence to gain speed. What exactly hurts when you try to spin faster? Do you have any pre-existing injuries or issues?

My general advice to get faster is to start riding with faster people. You have to be willing to push yourself, be it with intervals or joining a faster paceline. Long slow distance does have it's place in helping you develop a solid aerobic base, but it won't make you that much faster.

Have you ever had a professional fitting on your current bike? While the bike itself will only take you so far, there are tweaks you can make in your set-up that help you maximize your leg strength and comfort.

While I'm all for setting fitness goals, Í'd caution you against being overly competitive with your SO. I suppose some couples thrive on it, I'd venture to say most don't. In the very least, be supportive of your BF's progress without regard to how it impacts you. Hopefully, he'll return the favor.