Is it possible to get a set of phones that give sound characteristics of a good set of neutral monitors?
or is the wife gonna have to put up with my noise?
Eyup!
No, but it is possible to get the wife a pair of ear defenders 
Seriously, you can mix with headphones, but just like when you buy a new set of monitors, you have to get used to their little quirks and adjust accordingly.
I use a pair of cheap Sennheiser eH1430’s, although it’s still essential for me to finish off the mix with reference to my “monitors” (hi-fi speakers), car speakers and walkman-type earbuds.
Steve
"Don’t never ever use headphones for monitoring when you mix!"
Bullcrap!!!
Good near field monitors are OK for mixing, but don’t believe anyone who tells you that they give an accurate impression of what a typical listener hears.
And try this with your super zappo near-fields, play a mono 20Hz to 20KHz sweep through both speakers, and record it. The amount of spectral unevenness and comb filtering caused by reflection from VDU, desktop, ashtray…blah, blah, blah, will astound you.
And as for mastering, throw them nearfields in the trash! 
For mastering you need a large dead room and large studio quality monitors. And apart from your mastering console, nothing else at all.
So, who has all that stuff?
Not me, so it really is OK to use good headphones for mixing. They’re not perfect by a long ways, but neither are nearfields on a desk in a bedroom. So as Beefy says, learn how they sound by listening to lots of other material and get a feel for them; then send your mixes to a good mastering house for polishing. 