Omya,
Do you remember I told you the purpose for this prophecy/analogy? It was in response to the Pharisees and the teachers of the Law were ridiculing Him by saying "we want to see a miraculous sign from you." (matthew 13:38)
Jesus responded by pointing them to two things in that one verse
1. The Son of Man be in the earth for three days and three nights just like Jonah was in the belly of the whale. This was pointing to his death and the fact He would be three days in the earth,
2. You are correct there to, the Son of Man might have been dead in the earth, but the Son of God was very much alive... therefore the verse can also be read that even though He was dead.. and very much dead, so also as the God-Man Jesus Christ He was very much alive as God.
Again, it's essential to read my discussions on Jesus self proclamation as the God-Man.
Mind you, there is as I said before a third message here, which is by far the most important one in the context of this verse
The Jews had Jesus amongst them, yet all they could do was ask for miraculous signs. The Ninevites who had no Jesus amongst them repented, when Jonah preached to them and they will stand in judgement of those who know Jesus and yet reject Who He is.
This is by far, the most important message.