This に is a listing particle. See: Particle に to enumerate things?
高くも低くもない平均的な身長 is the same as 高くもなくて低くもない平均的な身長, or "an average stature which is neither big nor small". See: What is the correct grammar for "neither x nor y"? / How would you say "Something isn't X, but isn't Y as well."
- 高い身長: "big stature" ("tall height" is more literal but this is probably unnatural in English, so please bear with this)
- 高くない身長: "stature that is not big"
- 高くも低くもない身長: "stature that is not big nor small"
The omitted verb after 身長 is indeed だ/です (or をしている), but it has little to do with the grammar above.
短い黒髪に、高くも低くもない平均的な身長(だ/をしている)。
[He/She] has short black hair, and an average stature that is neither big nor small.
[He/She] has short black hair, and is neither tall nor short.