Travel medical coverage

I have Europe Assistance, and a couple of years ago they were great helping me when we were on holiday in the Caribbean and my daughter got ill. For rearranging travel, hotels and stuff for my family was a piece of cake. However, it is a bit of a hassle getting reimbursed for the healthcare costs, as you have to submit your expenses first to your mutuelle, who will then reject them, and then submit them to Europe Assistance. Basically they reimburse anything the mutuelle don't, but you have to have it rejected by the mutuelle first. It's a bit crazy, but I did get my money back.