Reservist Health Care Continuity Act - Requires employers to continue health care coverage for National Guard and reserve personnel called to active duty (and their dependents) for the lesser of: (1) an 18-month period or the day after the person fails to return to such employment, in the case of an employer with 20 or fewer employees; or (2) the period of such absence or the day after the person fails to return to such employment, in the case of an employer with more than 20 employees. Requires the Secretary of Defense to reimburse employers for the employer share of any premiums for such health care coverage for each month during such military service.