If co-applicants on a mortgage are not married, are we required to obtain separate applications?

No, and if you do you are discriminating based on marital status which is prohibited under Reg. B.

I guess I don't understand the OP's question. If you are in any way evaluating or extending credit differently dependent upon marital status, that would be illegal as a prohibited basis under ECOA. The logistics of completing an application - whether you have both applicants on one paper application or filling out two separate paper applications isn't the issue, it is in what manner the credit was requested and how the creditor evaluated the application, and applying that consistently to all applicants. Careful documentation of the applicant's acknowledgement and intent to apply jointly is important to avoid Reg B violations. Your underwriters should have systems to consider jointly owned assets (and liabilities) even if listed on separate paper applications. Think about it, if you had three applicants applying jointly, you're always going to have to use more than one paper application form.

From Reg. B 1002.1

(b) Purpose. The purpose of this part is to promote the availability of credit to all creditworthy applicants without regard to race, color, religion, national origin, sex, marital status, or age (provided the applicant has the capacity to contract)

From Reg. B 1002.4:

(a) Discrimination. A creditor shall not discriminate against an applicant on a prohibited basis regarding any aspect of a credit transaction.

If you require non-married applicants to complete separate applications where you do not married applicants then you are discriminating against the non-married applicants on a prohibited basis.

Additional documentation from the Commentary to 1002.4

Section 1002.4—General Rules

Paragraph 4(a)

1. Scope of rule. The general rule stated in §1002.4(a) covers all dealings, without exception, between an applicant and a creditor, whether or not addressed by other provisions of the regulation. Other provisions of the regulation identify specific practices that the Bureau has decided are impermissible because they could result in credit discrimination on a basis prohibited by the Act. The general rule covers, for example, application procedures, criteria used to evaluate creditworthiness, administration of accounts, and treatment of delinquent or slow accounts. Thus, whether or not specifically prohibited elsewhere in the regulation, a credit practice that treats applicants differently on a prohibited basis violates the law because it violates the general rule. Disparate treatment on a prohibited basis is illegal whether or not it results from a conscious intent to discriminate.

A better approach, I think, is to have your procedures such that you request a single combined application unless separate forms are needed to list or describe the individuals' separate assets. That could apply irrespective of whether the applicants are married (to one another or otherwise) or not.

Agree 100%. And ultimately the examiner will decide if there are any FL issues after a careful review of the creditor's own application procedures. Most creditors now don't have applicants physically complete applications - the LO interviews applicants and records information in an LOS, be it laptop, PC, iPad, etc. and we have data filling into an application template. I think with most LOS's, both applicants' data will fill into one application form unless as Mr. Burnett points out, the LO needs to identify assets owned individually. In any event, consistency in the application process and evaluation of the credit request is paramount to avoiding FL issues.