You can't do what you want without looping, since every key needs to be visited. In fact, you need three loops.

for every company
   for every employee of the company
   for every family member of the company
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But yes, you can use grep to loop.

my @companies = grep {  grep { $_ eq 'jim'  } @{$_->{EMPLOYEES}}
                     && grep { $_ eq 'bill' } @{$_->{FAMILY_MEMBERS}}
                     }
                keys %CompanyInfo;
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