Thanks everybody for you valuable inputs! I guess I will have to evaluate in the future about the costs of buying a home and renting, once I have the necessary equity.
I do love the idea of being able to modify the house to our liking and not having to revert it back for the landlord.
Either way, need to build up the finances for that first 
Thought I’d update this thread with more information for people who might be in a similar situation in the future.
As of of the 30th of April 2024, UBS offers the most comprehensive banking package for joint accounts in a Swiss/US household.
For CHF 15.- per month (based on a combined equity of CHF 10’000 across all three accounts), you each receive individual checking and savings accounts, along with respective debit cards. Additionally, you get two credit cards (Visa + Master) each and a shared checking and savings account with two debit cards.
After asking the advisor he will check if a third credit card for the joint account is possible. It’s worth noting that the standard credit limit is CHF 5’000. If a joint credit card is obtained, there might be an additional fee, and the CHF 5’000 limit would apply collectively to all three accounts, rather than individually. Will update this post as soon as I hear back from the advisor.
UBS provides both Visa and Mastercard options. The advisor mentioned a solution where, for example, one card (e.g., Visa) could be linked to the joint account, while the other (e.g., Mastercard) remains linked to the individual account. This way you and your partner might say that the Visa will be used for all shared purchases and the Master for individual ones.
UBS debit cards also offer a credit function and can be added to ApplePay, enabling the use of the shared debit card for everyday purchases. This feature was previously unknown to me and might require activation in the app settings.
So to summarise:
| Checkings Account | Savings Account | Debit Card | Credit Card | |
|---|---|---|---|---|
| Individual 1 Account | Yes | Yes | Yes | Yes |
| Individual 2 Account | Yes | Yes | Yes | Yes |
| Joint Account | Yes | Yes | Yes | No(?) |
As assumed, UBS does not let US individuals invest with them. I’m sure as a reader of this blog plenty of other solutions might look better anyway, but I thought I’d ask for completion sake