Pursue Each Others Interests
In addition to pursuing interests that are new to both of you, you can also build the friendship between you and your partner by pursuing things that are only of interest to one of you. This shows the other person that you truly care for them, because you're willing to go out of your way to understand them, and also gives the two of you even more things you can do together.
Why Pursue Something That You're Not Interested In?
For some people, the idea of pursuing interests that aren't their own sounds like an onerous task. There are, however, many good reasons to try and do so anyway.
First of all, doing something that wouldn't be your first choice of activities simply because it's important to your partner communicates a lot of things to them, all of them positive.
It says that they are more important to you than your own comfort level, and that you are willing to try new things simply because your partner is in your life. All of these will lead to a deeper friendship between the two of you.
Secondly, long-term relationships involve a lot of give and take. If you're not able to enter into this aspect of the relationship in something simple like spending an afternoon doing something you don't really like, you should consider how ready you really are for a more serious relationship.
Finally, one of the most important aspects of friendship is having things you can do with another person. If you know, at least at a basic level, how to do an activity that your partner enjoys, then it is one more thing that you can do together.
It may not be something you want to do all the time, but having it in your arsenal gives you one more tool for building a more committed relationship.
What If You Hate It?
Sometimes, your partner will be interested in something that you simply cannot pursue with them. Maybe you've tried skydiving and it made you ill, or you're allergic to plants and your partner likes to grow things.
When these situations arise, make sure your partner knows why you cannot pursue their interest with them. Express how much you care for them, and make an effort to make specific plans with them to do something else.
Then, allow your partner to go his or her own way and enjoy the chosen activity without you. Giving your partner this freedom can also communicate how important they are to you and that you want the relationship to be deeper and stronger.