First on the list is international property insurance. Personal effects and possessions taken into the host country are not covered by an employer's commercial policy. Furniture, clothing, ipod, and even the kid's toys needs to be protected globally and in the host country from fire, theft, vandalism, smoke, flood, etc. If a fire comes and your are out $100,000 don't expect the employer to step into the rescue. There are both legal and tax reasons why they cannot.
International personal liability needs to be purchased by the expatriate before the international assignment as well. This is basically "net worth protection" for the family as they live outside the home country. Although the incidence of lawsuit outside of the U.S. is lower than it is in the U.S., this coverage is still essential. One can cause damages for a variety of reasons that are not related to the work assignment. If not directly related to "work" the employer would not be able to step in and cover these personal lawsuits or damage awards. Good policies here also cover the legal fees in the host country and provide "trip" coverage back in the U.S.
Home country plans or vacant homeowners insurance in the U.S. only covers the dwelling. These policies would not cover the personal insurance needs of expatriates living abroad and separate arrangements need to be made past vacant home insurance.