What do you call an interfix that has semantic meaning?

Some disagree about the terminology, as should be expected, but semantic value is the distinction between an 'interfix' and an 'infix' in English.

An 'interfix' is

(linguistics) An empty morph inserted between two morphemes in the process of word formation, such as English -o-, -i-.

[interfix. (n.d.). Retrieved December 16th, 2015, from http://www.yourdictionary.com/interfix.]

For 'interfixes' the inserted morph has only a phonological value. Such morphs are represented in speedometer and humaniform.

An 'infix', also called an 'integrated adjective', has semantic value as denoted by the alternative term. 'Integrated adjectives' modify the semantics of the associated nouns, usually but not always by intensifying them:

An infix is a word element (a type of affix) that can be inserted within the base form of a word (rather than at its beginning or end) to create a new word or intensify meaning. Also called an integrated adjective.

(From "infix (words and grammar): Glossary of Grammatical and Rhetorical Terms" at About education.)

Examples of infixes include anyoldhow, absobloodylutely.

As quoted at the latter source, R.L. Trask in The Penguin Dictionary of English Grammar (2000) points out that the closest thing to a 'true' infix in English is the pluralizing -s in compounds:

English has no true infixes, but the plural suffix -s behaves something like an infix in unusual plurals like passers-by and mothers-in-law.

Trask's justification for excluding 'integrated adjectives' from the class of "true infixes", as well as his justification for excluding the plurals of compounds, are not readily ascertained from online sources.

The central disagreement about the terminology stems, again as might be expected, from a technical point. Hairs are split about the terms 'interfix', 'infix' and 'circumfix':

Technically, it also possible to have an infix (added in the middle of a stem), an interfix (in between two stems) and a circumfix (added on either side of a stem), but these are extremely rare in English.

(From The History of English, L. Mastin, 2011. Emphasis mine.)

By this definition, 'infix' is exampled by absobloodylutely, 'interfix' is exampled by anyoldhow, and 'circumfix' is exampled by unconsciousness.

The definition proposed suggests that 'integrated adjective' is not an sufficient alternative term for 'infix', and defines 'interfix' in contrast to 'infix' by morphological features rather than the presence or absence of semantic value.

Old post but could be helpful for others searching for some clarity with these two similar affix categories.

I believe JEL’s answer above is correct except that there’s a fundamental difference that separates affixes between infixation, interfixation and circumfixation.

The best way to identify an infix is that the stem word is split in two. “Abso-bloody-lutely” falls under this category. “Abso” and “Lutely” carry no meaning when split apart.

An interfix is different because it requires TWO stem words on each side of this affix placed in the center. So “Any-old-how” clearly includes “Any” and “How” are independent morphemes which can stand alone and still have meaning to them or be used in a sentence unbound.

Circumfix are very easy to identify because the stem will remain in the middle of the new word. Instead the affix will be attached at the front and end of the word. The hard part is differentiating a circumfix from a word vs. a word with both a prefix and suffix included. The only difference is that a circumfix will always be used together, in contrast to prefixes and suffixes being able to attach independently without the other present. Luckily, it’s mostly agreed upon that circumfixation is not very common in the English language but there are discussions and studies recently that would argue they are much more abundant that previously thought but it really blurs the lines between circumfixes and the inclusion of both prefix and suffix use.