That rent to price ratio is pretty meh, I'd personally be selling to put the equity to better use, unless you're expecting massive (above inflation) appreciation for a particular reason.
That aside, if you are keeping, the mortgage to value is quite low, so I'd just look at doing a HELOC to keep that low rate. Then again, I'd be looking for a 30-year, not 15, at a rate that low.
But based on you liking the 15-year, and presumably keeping this place, I'd go with a HELOC over a refi.
As another aside, splitting ownership, especially with someone you aren't married to, can be tricky. Have you considered letting her buy, and you just paying rent? You very likely come out ahead, monetarily, due to the opportunity cost on the money (even paying rent, rather than building equity), based on those price-to-rent ratios in your area.