Your data structure seems to be wrong. You show something that could be described as HoHoH, but I suspect you should really have a AoHoA. Consider:

use strict;
use warnings;

my @records = ({
        EMPLOYER                 => "Widget Co.",
        EMPLOYEES                => "jim",
        EMPLOYEES_FAMILY_MEMBERS => ["susan", "bill"],
    },
    {
        EMPLOYER                 => "Widget Co.",
        EMPLOYEES                => "john",
        EMPLOYEES_FAMILY_MEMBERS => ["liz", "bill"],
    },
    {
        EMPLOYER                 => "Foo Ltd.",
        EMPLOYEES                => "jim",
        EMPLOYEES_FAMILY_MEMBERS => ["karen", "bob"],
    },
    );

my @selected = grep { "@{$_->{EMPLOYEES_FAMILY_MEMBERS}}" =~ /bill/ }
  grep { $_->{EMPLOYEES} =~ /jim/ } @records;

print "Found ", join (", ", map { $_->{EMPLOYER} } @selected), "\n";
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Prints:

Found Widget Co.
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