Can you buy family insurance?

Because insurance is based on the assessment of risk, you usually have to insure individuals, as individuals.
There are a few areas where you can buy insurance on a family basis. Just take care as there is no guarantee it is cheaper to buy as a family. Travel insurance is sold to families and groups, some offering a kids go free deal, but do check if it is cheaper to buy in one go, or just more convenient.
The quote process looks the same with number and age of people being necessary. You should expect some small discount if you are buying a group policy rather than one for each family member, but it will not be much, as the risks to the insurance company remain the same.
Most policies are sold as family protection. Life cover, or term insurance, are sold to you by saying what will happen to your family if you are no longer there to provide for them. So here you would arrange an individual policy, rather than a family wide policy.
Insurance is sold to the family, rather than being arranged in family products. That is not surprising as insurance is based on assessing risks, and individual risks in particular.
If you do come across good cover competitively priced for the family please let us know.