Can one ex-spouse take out a life insurance policy on the other ex-spouse? 

In order to own and pay for life insurance a person must have what is known as an "insurable interest." Insurable Interest has been defined as the requisite connection between the owner/payor and the person whose life is insured.  This requirement usually demonstrates that the purchaser will actually suffer some kind of loss if the insured dies; for example, as in the case of a financially dependent spouse or former spouse and children in the life of a former spouse.  If your husband's ex receives alimony or if she receives child support, then she has an insurable interest;  otherwise, probably do not.  Possibly their divorce decree addresses this issue? To be certain of your rights under state law, you should discuss this matter with a local attorney or at least contact your state's Department of Insurance.