To begin with, you should see what are the strong sides of yours and your co-GM candidate and try to make use of those aspects of your GMing in order to compensate the weaker sides of each other.
Let me provide some orthogonal aspects of a good GM I see over years of playing games. You can even stylize those as a list of abilities and make GM-sheets, rating each others' abilities in the areas of interest.
- STR: Storytelling. Shows how well can you use the language to speak about events, how detailed and colourful picture of the surrounding world you can inject into players' heads. Also, describes the overall interestingness of your modules and campaigns.
- PRP: Session and module preparation. Shows how well you are able to prepare to a session, how detailed your module is, etc. Can be thought as "playing against players". You need to make challenges, puzzles and the storyline in such fashion that it's not a cakewalk for the party.
- IMP: Improvization and adjusting the plan to the events that ocurred. One can think about this one as "playing with players". Shows the degree of interactiveness of your world.
- RAW: Rules-as-written. How well do you know the rules as written and erratas from the main books, complementary books, et al.
- GLD: The Golden Rule™ usage. Are you good at making decision of throwing in the Golden Rule™? Can you handle munchkins? Those are things that this ability shows.
- PXP: Playing experience. How many campaigns of the given system have you played? How well can you understand your players? This is yet another "coodrinate" in our system.
As a rule of thumb unless you have a large experience of GMing together you want to divide the roles and as the main GM, you want to have STR and PRP on you.
Here is a suggestion that's supported by my own experience:
If you want to run a session or two with co-GM with little to none preparations, just let your co-GM run some key NPCs (making use of GM's high IMP ability); let your co-GM to calculate the combat (making use of his high RAW ability) and finally let your co-GM to decide for NPCs in combat (if he has a high PXP score in addition to a high RAW score).
As for the question about collaborative improvisation I would strongly suggest against it. You shouldn't do that until you are sure that you understand each other perfectly and will not mess up with each other's plans, bringing discord in your game.
However, over time, as you talk more about the campaign and get better synergy, you'll be able to offload more creative tasks to your co-GM if you two will wish so, including improvising together.
An example of collaborative improvisation would be a case when you — as a GM — need time to think a little bit about some tweaks to the storyline on the fly. In order to do that, just signal co-GM to take over and (given that you understand each other well enough) you'll be able to retake mastering of the game after you have made all the tweaks you needed.
Hope that helps.