If your parents purchase the policy, they do not need to prove insurable interest because they will be the owners of the policy and the insured. (truebluelifeinsurance.com)
The next step is usually proving insurable interest as well as consent. (bestliferates.org)
Once again, I will reiterate that you need to prove an insurable interest exists should your partner pass away. (insuranceblogbychris.com)