I have attended a church that did it this way, a long time ago. I do not agree with the idea for a couple of reasons.
First, when Jesus initiated the Supper there was a separate emphasis on His body and His blood. He made a point to talk about His body given for us - suffering through the agony of the Garden and the crucifixion, and bearing the wrath of God for our sin. Then He made another point about the New Covenant in His blood shed for us. The shedding of blood of course a reference to His death in paying the penalty for our sin.
So we have a remembrance of His suffering and then a remembrance of His death. He distinguished them as such upon initiating the meal.
To join these together seems to de-emphasize what Jesus was showing us in the Supper. At least that is what happened at the church of which I was a part.
Another problem I have is the use of leavened bread for the Supper. (Unless the church is dipping unleavened bread in the wine.) In the Bible leaven usually (not always, but mostly) signifies sin, hence the Passover as it was ultimately fulfilled in Christ gives us unleavened bread....Jesus the bread of life....unleavened, having never know sin yet becoming sin for us.
I do not know where this practice came from, but would be interested to hear what churches use it!
At ours, we do not.
Phillip