Yes, 3 branches (just the standard separation of powers) and 3 “levels” (with the judicative branch 4 depending on the case).
Swiss and US system is very similar. The big and important difference is the election system. The US has the shitty system that forces a two-party-situation over the years. We have a more proportional system, where you vote for a party (actually a list by a party but thats a detail) and for candidates. Then the seats are spread to the parties, if your chosen party doesnt win a seat, your vote isnt wasted (which would then require strategic voting which leads to two parties). Your vote is passed on to another party. Which one that will be, your party decides. So if you vote for “radical-left-party” and its members, this vote isnt wasted bit goes to another leftleaning party, which has a “Listenverbindung” (Joint up lists) with the “radical-left-party”.
And of course we have direct democracy (voting often on singular laws, also statewide/canton/communal) and we dont have gerrymandering but just the normal division into “Gemeinden” (literally “community”, which would be a county? or village/city in the US).