Currently, you're unable to add a membership to someone who takes an action on an invoice page. This is a feature that is available for most other page types. It would be great if you could connect memberships to invoice pages to allow for people to purchase memberships using those pages instead of donation pages. This would allow us to better distinguish between a membership *payment* and a donation gift.
Thanks Dana - this is a great suggestion thank you - we don't have any immediate plans to update invoices but this is very helpful and I will let you know here if there are any updates.