It's not *exactly* what you're asking for, but might be useful to know about if you can't find exactly what you want...
I made double-sided calendars every year for family and friends too, and what I use is inkjetart's Premium Duo-Brite Matte paper. It's a fairly thick and reasonably stiff double-sided matte paper; I know that you'd prefer paper that isn't fully matte, but I find that this surface works very well for writing on (for people like me who make notes on their calendars). It's also quite inexpensive compared with most papers, but it still looks quite good for a matte paper. (If you'd prefer slightly less expensive still, they have two slightly cheaper non-premium varieties of the Duo-Brite Matte, but the Premium has slightly better Dmax and is only slightly more expensive, and I think it may also be slightly thicker.) It comes in 17"x22" (though I use the 13"x19", personally); not sure about rolls.
You can find it at inkjetart.com. inkjetart also has numerous sample packs of various papers so you can try several, which is how I originally decided on this one. Caveat: I use Epson printers, so no guarantees that it will work well with your particular printer, but that's what sample packs are for.
Lisa