What ever you want so long as it is “adding value” for visitors. Pretty simply, your main site should link to your blog in the header or footer (which makes it run of site) and your blog should like to eCommerce site in either the head or the footer (run of site again) plus wherever it makes sense such as product mentions, coupons, promotions, etc.
Google is not going to treat these two domains as anything different than it would if it was one domain
Remember that the ranking algorithms do not rank ‘sites’ – they rank pages and pages are not even known internally by their name but by an arbitrary DB index, instead.