What is the Catholic understanding of the first sin committed by Adam and Eve? I always used to consider the first sin committed by Adam and Eve as eating the forbidden fruit from a particular tree. But recently my husband commented that Adam and Eve had sex with each other which is the first sin. I had no substantial point to prove against his point.

Is sex considered to be the forbidden fruit? Is that thought prevalent among Catholics? What is the Catholic teaching on the first sin of Adam and Eve?

(Note that this question is asking about the first sin committed by Adam and Eve, not the doctrine of "original sin": that we all in some way have inherited a sinful nature from them.)
Sexual intercourse was not a sin at all (for Adam and Eve in the context of their marriage).  In fact, God commanded them to be fruitful and multiply:


  "And God blessed them. And God said to them, "Be fruitful and
  multiply and fill the earth and subdue it and have dominion over the
  fish of the sea and over the birds of the heavens and over every
  living thing that moves on the earth."  Genesis 1:28 ESV


While having sexual intercourse was not a direct command, it most certainly was an indirect command.  You can't be fruitful and multiply without it, unless God was merely encouraging them to garden and do arithmetic.

So, the original sin was eating of the fruit in direct violation of God's command.  However, it could be suggested that pride preceded that, because for them to defy God's command they had to exalt themselves as the authority over their own lives.  Pride would have been a sin of the heart whereas eating of the fruit was a sin of deed.