I’m not the best person to answer, since I haven’t carried a mug for years (I also cook only for me: add boiling water to the freeze-dried bag, then heat tea water in my small 700ml pot and drink from the pot - clearly not feasible for you.)

Will it keep the coffee warm? Depends on how fast you drink it. (Sorry, couldn’t resist.)

One thing that you might take a look at is a cozy for a titanium mug (visit AntiGravityGear’s website - they may offer such cozies, or at least a kit.) The advantage here is that you can use the mug to heat water (at lunch, or a break on a cold day), then put it in the cozy to keep it warm. Some people love cozies, some hate them.

Depending on how you and your partner cook, you might want to just get a second Jetboil pot for your stove. Then each of you can have an insulated mug that you can cook in. (If you use the freezer bag method, you could boil a pot and use it to add food to your pack, then boil another pot and split it for coffee or tea - or even boil two pots, so you each have a full liter of beverage.)

Also, take a look at the MSR Windburner stoves - they’re a Jetboil clone, but some reviewers say they are slightly more wind-resistant and fuel-efficient. You can also buy spare insulated pots for these, too. I don’t have enough experience with Jetboil or Windburner to notice any difference. (I use a “plain” canister stove and put it behind a log or the downwind side of my body to block the wind.)

Others can fill in the gaps in what I’ve written; like I said, I’m not an expert on mugs.