Is this query possible?

Hello all,

I have a MultiSearcher searching two separate indexes.

One of the indexes (index B) has some extra terms in its documents 
compared to the other (index A).

Consider this scenario:

Index A documents:
field: fulltext

Index B documents:
field: fulltext
field: visible

I want for a query such as :

fulltext:"car" AND visible:1

To return all the matching "car" results in Index A, thus ignoring the 
'visibile' constraint if it's not defined for the document. How can I do 
that? Right now the results completely skip Index A because of no 
matching 'visible' field.

Thanks.