A frustrated curse on both sides of an argument.
From Shakespeare's Romeo and Juliet, 1592:
I am hurt.
A plague o' both your houses! I am sped.
Is he gone, and hath nothing?
The houses are those of the feuding Montague and Capulet families, which caused Juliet so much grief and was the source of her 'O Romeo, Romeo! wherefore art thou Romeo' speech.
Shakespeare was fond of the word plague and used it hundreds of times in his plays. Surprisingly, as the Bible is the other most prominent source of phrases that have entered the English language, there isn't a single use of the word 'Bible' in any of his plays.
The tradition of displaying blue plaques on the houses once lived in by notable persons, now administered in the UK by English Heritage, leads to a nice play on words relating to Brook Street, Westminster, London. Jimi Hendrix lived at number 23 and George Frideric Handel lived at number 25. The current residents have a plaque on both their houses.
See other phrases and sayings from Shakespeare.