The most his company can charge is 102% of the actual premium with the extra 2% being an option addition to cover administrative costs.

The problem for you is that the total cost of the insurance has not been something you were aware of until now. Most employers who provide health insurance pay for the majority of the cost with only a fraction being charged to the employees. The percentage the employer pays vaires susbtantially between employers and can range from 100% to zero, with an average being around 70% to 80%. So some people 'think' their coverage is expensive because it is a few hundred dollars a month even though the total cost including the employer paid portion can typically be anywhere from $1,000 to $3,000 depending on the type of coverage and the number of any dependants of the insured being covered.

Suddenly when an employee leaves a job they have to pay 102% of the employer's cost instead of some small percentage.

As an alternative your family should look at getting insurance through the federal marketplace (healthinsurance.gov). The job change likely qualifies your family for a Special Enrollment Period and the cost might be much lower, although the plan might not cover as much and might have higher deductibles, and you might qualify for a federal credit to reduce the premiums. So check it out at healthinsurance.gov or by contacting a local health insurance agent.