Facets and Search box on the same page
Inputs: Sitecore 8 Update 3. Coveo for sitecore: Sitecore Integration 3.0 September 2015 Release. Free edition for dev purposes.
I have a common site with header with a searchbox and two columns body. Header contains "SearchBox" (out-of-the-box Coveo component) and left column contains Facets List component (custom component created with only facets, created by https://answers.coveo.com/questions/4985/standalone-facet-without-a-search-box answer).
At the beginnig, I had a problem, with more than one Coveo component on the same page. But I found how to resolve this problem with: https://answers.coveo.com/questions/4830/adding-search-box-hides-the-coveo-search-sublayout answer.
Now I have another problem: SearchBox loads as a part of "Facets list" component. When I type within SearchBox and press Enter, instead of redirect to the "search" page, I get update of Facets list. Which is not what I expect.
How can I run two Coveo Components on the same page, but in a separated scopes/behaviour?