According to Merriam-Webster:
penetrate — to pass into or through
compenetrate — to penetrate throughout
What is the difference between the two? Are they synonymous?
I don't think they're synonymous, no; one suggests a more complete level of penetration than the other. Judging by the definitions, I'd guess that you'd penetrate through, but you'd compentrate throughout.
I initially wondered if compenetrate is a word used in a specialized field (perhaps something scientific, e.g., to describe how an electrical field might compenetrate throughout a substance), so I did a search on Google books.
What I found was rather instructive. First, the word is indeed rather rare (only 75,000 hits, versus more than 12 million for penetrate). More significantly, it appears to be a word used almost exclusively in the realm of philosophy – a great preponderance of the cited references were scholarly works in philosophy or religion, such as:
As I perused through the results, a few quotes kept appearing over and over again, such as:
This quote, along with some others that were oft-repeated, was attributed to turn-of-the-century philosopher William James. I saw the word appear in so many references to his writings that I began to wonder if he coined the term, but the OED refuted that theory:
My spellchecker doesn't like the word. There's probably very little need to use the term, outside of esoteric philosophical writings discussing various levels of consciousness and subconsciousness, parallel universes, and the like. I can think of very few everyday uses for the word, although I suppose it might be apt if you were trying to describe the compenetrating Vulcan mind meld that Mr. Spock gave to Dr. McCoy.
The two words are synonyms. However, compenetrate is a very rare word which will be understood by almost no one. Stick with penetrate.
This Wordnik definition of compenetrate says it is "to penetrate every part of." So yes, they are synonyms. The example sentences given in the word's entry on this site appear to be mostly from philosophical fields. (Note that at the bottom of the entry, there are no "related words.")
The Wordnik entry for penetration gives a dozen or so definitions. The example sentences range from the philosophical to the very tactile (a wasp sting). There are several columns of "related words" for penetrate. This shows (and I agree with JSB) that penetrate is a much more commonly used word.