(a) An employee eligible to receive reemployment assistance benefits under section seventy-one F shall also be eligible to receive health insurance benefits during his or her eligibility period if (1) the individual was, at the time of termination covered by an individually purchased health insurance plan, and (2) the individual is not able to be covered under any health insurance plan carried by a member of the family.

For the purpose of this section, the eligibility period shall commence with the effective week of the claim for regular benefits and end at the completion of three calendar months, or the completion of the month during which reemployment was obtained, whichever is less. The payment of health insurance benefits shall terminate at the end of the month during which employment was obtained.