If you are living with your spouse or a common-law foreign national partner, and that person satisfies the above requirements, then both of you can decide who will apply as a principal applicant under Express Entry.
A common-law partner is someone that has lived with you in a conjugal union for a period of one year. This applies to both same-sex and opposite sex couples.
Take a look at the selection factor and determine who among you meets the eligibility requirements. He/she should go ahead and apply as the principal applicant.