if yes, especially what parts should they determine together? (Layout?, grid?, information architecture?)
The UX Designer, in my experience, is responsible for creating wireframes. However, you'll collaborate with everyone on the project team as you do it.
I've worked on fancy sites where the UI designer drives the design, with my push-back to keep it simple, clear, and intuitive. We collaborate on interaction effects and page layouts. (I've never determined a grid myself - that's always been their decision.) They're usually more in touch with the latest interaction techniques. But still I'm the one wireframing, documenting our decisions.
In other cases I'll share my first draft with the devs, UI, project managers, etc. - still collaborating, though I'm driving the initial design process.
You'll collaborate, not just with UI Designers, but the entire product team. (And do user research, of course), but ultimately you'll be the one who creates the wireframe documents.
(Is the UI Designer stepping on your role?)