There really is no hard and fast rule on this. Both of you getting sober is definitely a great goal to have. You might find that going to meetings together is helpful, but then again you might want to go on your own in case you would like to be truly anonymous with others about it. Or you could do both....there's nothing stopping you from trying it.
Co-dependence can be a big issue though - encouraging/enabling each other to drink on special occasions, etc. In that sense you will honestly need to internalize and commit absolutely to your sobriety as an individual at times...so you can say NO when the other half wants to throw in the towel for the day.