What is the Roman Catholic interpretation of John 3:16?

Let us not forget context. Much error can be avoided if we remember the context in which Scripture verses are written. John 3:16 is the continuation of Yeshua's conversation with Nicodemus that began in John 3:1. It is Pesach (Passover), and the conversation Yeshua and Nicodemus are having involves the nation of Israel. In John 3:3, Yeshua says, unless one is born again he cannot see the Kingdom of God. The word "again" is G509, and it means "above", not "again". So, the verse should read, unless one is born from "above", he cannot see the Kingdom of Elohim (God). The phrase, "The Kingdom of Elohim" (God) is a reference to the Throne of David, the House of Jacob, which is the Kingdom of Elohim (Luke 1:32-33). Where is the site of David's throne? It is Jerusalem (I Chronicles 14-17).

In John 3:14, Yeshua mentions Moses and the serpent in the wilderness. Who was that story about--the nation of Israel. So, when Yeshua speaks of the world, in v.16, He refers to Israel. The word "world" is G2889. Yes, it does mean the world, as in the global world itself, but it also means an orderly arrangement, a region with borders; a territory. And in this case, it refers to Israel, since that is the territory Yeshua and Nicodemus were talking about. They were talking about Israel, not the world at large. The word "perish" is G622. It means destruction, but it also means to sever from its source. So, Elohim so loved Israel, that He gave Israel His Begotten Son (Yeshua is the Kinsmen Redeemer of Israel only), that whosoever IN ISRAEL, believeth in Him will not be severed from the nation of Israel, but will have everlasting life...

John 3:16 tells us that:

God gave His only begotten Son, Jesus, to live for us and die for our sins on the Cross (see also Romans 5:8)

• We must believe in Jesus in order to have eternal life. The word “believe” means that we must commit our life to Him and follow Him as our Lord and our God.
• Believing in Jesus means we will not “perish,” meaning we won’t spend all of our life and all eternity separated from the presence of God in hell.
• When we turn our life over to Jesus by believing in Him, He gives us “everlasting life.” Everlasting life begins the moment you believe in Jesus and begin to follow Him, and it continues into heaven itself.

The simplest answer, Catholic or otherwise, given the context would be that the word "perish" here means hell.

The Catholic Church does not usually have official interpretations of individual scripture passages, Catholics view the bible as a whole. For example if you view this passage alone you can say that all you need is to believe in Jesus and you will not perish. But reading on in the same chapter (verse 36) we see "He who believes in the Son has eternal life; he who does not obey the Son shall not see life, but the wrath of God rests upon him" This passage adds more meaning to John 3:16. Here obedience and faith play role in salvation.

Of course just because the Church does not have an official interpretation of each bible passage that doesn't mean that individual Catholics can't interpret the passages by themselves. As long as they stay withing the Catholic faith and using the four senses of scripture as outlined in answer by Peter Turner.

I can't answer for the Catholic interpretation of Perish in John 3:16, but I can give you the Catholic approach to reading the Bible and my opinion of that. It's all pretty obvious and doesn't help, but should shed light on why this is an unanswerable (yet good) question.

The four senses of scripture

1. Literal

   John 3:16 literally means "shall not perish", the same way Jesus said to Peter later in the Book that the disciple whom He loved might live until He returns.

2. Moral

   John 3:16 instructs the faithful just how much God the Father loves His children. If you love someone you will make the ultimate sacrifice for them.

3. Metaphorical

   Perish could mean die a spiritual death as easily as it means die a physical death. To die in ones sins, would be a metaphorical interpretation of the word perish.

4. Eternal

   Here's where perish means, suffer the fire of hell and that would be true too.

So, there's 4 legitimate ways of looking at the same piece of scripture neither of which negate the other, neither of which are authoritative.