Sorry to sound pedantic and ''Englishteacherish', Jack, but the words you are using in your current rebus are actually 'compound' words rather than 'portmanteau' words.
A portmanteau word is when a new word is formed from parts of two other words; for example 'brunch' is made from 'breakfast and lunch
I refer you to the author of my second favourite book, courtesy of Wikipedia:
The word portmanteau was introduced in this sense by Lewis Carroll in the book 'Through the Looking-Glass' (1871), where Humpty Dumpty explains to Alice the coinage of unusual words used in "Jabberwocky". Slithy means "slimy and lithe" and mimsy means "miserable and flimsy". Humpty Dumpty explains to Alice the practice of combining words in various ways:
You see it's like a portmanteau—there are two meanings packed up into one word.
In his introduction to his 1876 poem 'The Hunting of the Snark', Carroll again uses portmanteau when discussing lexical selection:
Humpty Dumpty's theory, of two meanings packed into one word like a portmanteau, seems to me the right explanation for all. For instance, take the two words "fuming" and "furious". Make up your mind that you will say both words, but leave it unsettled which you will say first … if you have the rarest of gifts, a perfectly balanced mind, you will say "frumious".