This modern form ["is being ..."] is very seldom used among writers of the highest class.... “The house is being built” does not express what is intended; being built denotes existence in the state experssed by built; as, “Our house being built, we have now a home.” It would be better for those who are not satisfied with the well-established classical form ["The house is building"] to say, “The house is becoming built” — coming into the state expressed by built.
Thanks to Prof. Mark Liberman (Language Log) for pointing this out. (He reports that “the progressive passive [e.g., 'is being built' -EV] first appeared in the English language in the second half of the 18th century, replacing what historians of English grammar call the passival [e.g., 'is building' -EV].”
Today, of course, “the house is building” (or, to give another example offered as proper in the late 1800s, “While these arrangements were making”) is so rarely used that it is likely nonstandard, or at least highly unidiomatic, and “the house is being built” is fully standard. And we say “the house is being built” because we wisely adhere to Horace’s advice: Follow “the will of custom, in whose power is the decision and right and standard of language.”