Your question raises two issues: the conflict of interest question and the appropriateness of the transaction question.  The conflict of interest issue probably depends on the Conflict of Interest policy of the lending or investing organization.  Most conflict policies will require recusal from the decision on the transaction and administration of the transaction on behalf of the lender/investor by anyone who has a conflict by virtue of being a member of the governing body of the other side of the transaction.  (See Ready Reference Page: “Conflict of Interest Policies Help Avoid Problems”)  The signature of the conflicted person will normally not invalidate the transaction if it has been approved by the board knowing of the conflict and the director has authority to sign for the organization.  Assuming you are a public charity that files a Form 990 or 990-EZ annual return, you probably won’t have to report the transaction on the return unless the receiving organization is related to yours or one or more of the officers or directors of your organization control 35% or more of its voting power of the other organization.  In short, it is not the best idea to have the conflicted director sign the documents and could offer fodder for critics if the deal goes bad, but it is probably not illegal.

The terminology of a “program related investment” comes from the private foundation world, not the world of public charities.  Program related investments may be counted as qualified distributions to help a private foundation meet its 5% payout requirement under certain conditions, one of which is that the investment is not intended to produce significant income or capital appreciation.  In that context, a no-interest loan is clearly not intended to produce income and is more likely to qualify as a PRI than a market rate loan to the same organization.  Either transaction would be a loan, however.  Assuming again that your organization is a public charity, the nomenclature applied to the transaction has no legal significance for you.  Your board has a fiduciary duty invest its funds reasonably, and to the extent that it is investing at significantly below-market rates, it should have a mission-related reason to do so.