Multi-index searches without Solr?
Only Solr supports that functionality. What you need is: 


Create a server in Search API, call it, for example, "solr_server". 
Create two indexes, one for nodes another for taxonomies. Make sure both indexes belong to "solr_server"
In views (make sure that search_api_views module is enabled), select 'solr_server' from Show dropdown list.
Now you can add fields from every index, that belongs to "solr_server".


Hope this helps.