The answer, as with most questions, depends on how one defines the terms.
If "omnibenevolence" means that God is always and perfectly desiring "the good", then yes, God is omnibenevolent (Mark 10:18; Romans 12:2). If, on the other hand, it means that God is always and only desiring the eternal and ultimate happiness of all humans, then no, God is not omnibenevolent (1 Samuel 15:2-3; Genesis 6:7).
In Christianity, that-which-is-good, namely the glory of God, does not equate to humanism's version of that-which-is-good, namely the glory of man, even though most of us humans want it to.
As a result, the Christian God does not necessarily seek to put humans at the apex of His thought, because, frankly, we don't belong there, and God is too smart to make that idiotic mistake. Humanists cry foul when they are not considered the most important thing in the universe by any god, including the Christian God. But Christianity (just like any other worldview) would be necessarily incoherent if it taught, as humanism does, that humans were the measure of all things... since we plainly are not.
Many would argue that if God is omnibenevolent, as Christians assert, then He would never send anyone to hell. However, this is to misunderstand the Christian claim -- it is to merge Christian ontology with humanist values, thereby creating a straw man. Humanist values, elevating humans above all things (including God Himself) are absurd on the face of them, and have absolutely no part in Christian thought.
Our omnibenevolent God instead glorifies Himself first and foremost (Isaiah 48:9; Ezekiel 20:9; Matthew 19:29, 24:9), as He should, since He Himself is the ground of all being (Exodus 3:14; Genesis 1:1; John 1:3) and the author of all legitimate ethical standards (Malachi 3:18). God Himself is the measure of all things, and "the good" is that which glorifies Him. Since it glorifies Him to punish sin, and since glorifying Him is the ultimate in goodness, it follows that of course an omnibenevolent God will punish sin.
If you have ever sinned -- and you have -- this creates a problem for you (Romans 3:23).
In fact, the Bible says that "the wages of sin is death" (Romans 6:23). Death is what we deserve for our disobedient behavior. But it doesn't end there. The Bible also says that "the cowardly, unbelieving, abominable, murderers, sexually immoral, sorcerers, idolaters, and all liars shall have their part in the lake which burns with fire and brimstone, which is the second death" (Revelation 21:8). We not only deserve death -- we deserve hell.
However, the good news is that it also glorifies God to forgive sin! God has offered forgiveness of sin to all who put their faith and trust in Jesus the Christ, the Son of God. As Christ Himself said, "I am the resurrection and the life. He who believes in Me, though he may die, he shall live" (John 11:25). Christ promised that if we believe in Him, we can escape the second death. This is quite a promise, but why would anyone believe it?
Christians believe it because of another absurd promise that Christ made, one that we see from history that He actually made good on. He told His followers, "The Son of Man is being betrayed into the hands of men, and they will kill Him. And after He is killed, He will rise the third day" (Mark 9:31). To prove that He was as good as His word on this point, and on every point, when He Himself was executed for blasphemy because He claimed to be equal with God, He then raised Himself from the dead as He promised, thereby conquering death, demonstrating that when He had claimed to be the resurrection and the life, He actually had the credentials to prove it.
According to scripture, if we confess with our mouths that Jesus Christ is Lord, and believe in our hearts that God raised Him from the dead, we will be saved from the second death -- the fiery torment of a very real hell. (Romans 10:9)