While we do not have a list of the insurance companies that will allow you to have an insurance policy without listing your spouse on it, there are some that will permit this. Since your husband is a household member if you choose to get your own policy separate from him, you will need to find an insurance provider that will exclude him from your policy.
In general, insurance companies do not tend to want to exclude a spouse who has been licensed since they usually require all licensed household members to be listed on the policy. It is unfortunate for those with good driving record whose household members have accidents or poor driving records since this can affect the household's insurance rates.
If a person, such as your husband, has a bad driving history it can affect influence your premiums due to the fact that he resides with you and may drive your vehicle. A person with a bad driving record of is more of a risk for an insurance company then a person with a clean driving record and thus their rates are normally higher.
You can get an auto insurance quote here with us to see if we can provide you with the type of insurance policy you are looking for.