Is it possible to transfer characters between Steam accounts?

Solution 1:

No, there does not appear to be any way to transfer save data between Steam accounts, for good reason. Just search for "payday 2 save" on Google, and you'll see what I mean.

OVERKILL doesn't want people using pre-made or modified saves, and have thusly, made it very nearly impossible to modify them (though not technically impossible, since save data is stored on the client-side). It would appear that among the information that the save file stores, your SteamID is part of it, to keep people from using "LEVEL 100 ALL PERKS ALL MASKS ALL WEAPONS $1 BILLION CASH" save files off the internet.

Solution 2:

No, Steam Family Sharing is set up so that each account has their own cloud saves, achievements, etc.

For a game with transferable saves (e.g. Neverwinter Nights 2), you would have to manually copy the save files from one computer to the other. Payday 2 locks your save to your steam profile, so short of a save game editor transferring saves will not work.