Trust Each Other's Decisions
Bicycle touring is all about choices. There's the decision of where you are going to tour, what gear you're going to bring, what you're going to eat, where you're going to stay, whether or not that log bridge will hold your weight, etc. If your partner feels strongly about a certain choice, trust their judgment and go with it.
Speak Highly of Each Other Around Others
On the road, you're bound to meet a lot of interesting people. When you do, be sure to speak of your partner in the highest regard. You would appreciate the same courtesy from your partner, and as a bicycle touring team, anything negative you say reflects back onto you, so pour on the compliments!
Everyone loves surprises, especially when they are feeling down. If you've gone through a couple rough patches on your trip, pick the mood back up with a fun surprise. It doesn't have to anything fancy, and certainly not large since your carrying space is limited. It can be as simple as a secret detour to an ice cream shop, or hauling around a two liter bottle of grape Fanta on a hot day.
Split the Tasks
Everyone has their strengths and weaknesses, so keep those in mind when you're planning out your daily tasks. For instance, if you're a poor cook, you can always pitch in by cleaning up after meals. If you would rather not set up the tent, you could scavenge for wood and get a fire started.
Plan a Zero Day
Depending on how long your tour is, you'll want to have some zero days built into your itinerary. These are days with zero miles, where you just kick back and relax. It's a great opportunity to collect your composure, take in some alone time if you need it, and prepare to hit the road anew. If you can, try and plan your zero days somewhere exciting.