The policy framework for libraries, archives and museums has come together in several contexts, although actual services have not converged much. IMLS in the US, MLA in the UK, and other bodies have cross-domain responsibilities. I have just come back from visiting the newly formed Library and Archives Canada, but that is as yet an untypical organization.
I always think that the availability of good words for talking about something is a sign of acceptance and maturity. In this case we do not yet have good words. We have 'memory institution' or 'memory organization' (given currency here), or the vague 'cultural institution'. We also have some acronyms (GLAM - galleries, libraries, archives, museums; ALMs; ...) that are too twee to really use.
This in the context of an interesting paper by King and Hedstrom I have just come across which puts the development of Libraries, Archives and Muesums (which they call LAM) in an interesting perspective.