This doctrinal concept is probably misconstrued as the Doctrine of the Trinity. However there is scripture to support this where there isn't any for the DOTT.
This is the main supporting scripture: I Thes. 4:13 ¶ But we would not have you ignorant, brethren, concerning them that fall asleep; that ye sorrow not, even as the rest, who have no hope. 14 For if we believe that Jesus died and rose again, even so them also that are fallen asleep in Jesus will God bring with him. 15 For this we say unto you by the word of the Lord, that we that are alive, that are left unto the coming of the Lord, shall in no wise precede them that are fallen asleep. 6 For the Lord himself shall descend from heaven, with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first; 17 then we that are alive, that are left, shall together with them be caught up in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord. 18 Wherefore comfort one another with these words.
I also include:
Mat 22:1 ¶ And Jesus answered and spake again in parables unto them, saying,
2 The kingdom of heaven is likened unto a certain king, who made a marriage feast for his son,
3 and sent forth his servants to call them that were bidden to the marriage feast: and they would not come.
4 Again he sent forth other servants, saying, Tell them that are bidden, Behold, I have made ready my dinner; my oxen and my fatlings are killed, and all things are ready: come to the marriage feast.
5 But they made light of it, and went their ways, one to his own farm, another to his merchandise;
6 and the rest laid hold on his servants, and treated them shamefully, and killed them.
7 But the king was wroth; and he sent his armies, and destroyed those murderers, and burned their city.
8 Then saith he to his servants, The wedding is ready, but they that were bidden were not worthy.
9 Go ye therefore unto the partings of the highways, and as many as ye shall find, bid to the marriage feast.
10 And those servants went out into the highways, and gathered together all as many as they found, both bad and good: and the wedding was filled with guests.
11 But when the king came in to behold the guests, he saw there a man who had not on a weddinggarment:
12 and he saith unto him, Friend, how camest thou in hither not having a weddinggarment? And he was speechless.
13 Then the king said to the servants, Bind him hand and foot, and cast him out into the outer darkness; there shall be the weeping and the gnashing of teeth.
I also include the harvest of wheat (Righteous people) in the Rapture coming before the harvest of tares (un-righteous people) that comes with fire:
Rev 14:15 And another angel came out from the temple, crying with a great voice to him that sat on the cloud, Send forth thy sickle, and reap: for the hour to reap is come; for the harvest of the earth is ripe.
16 And he that sat on the cloud cast his sickle upon the earth; and the earth was reaped.
17 Another angel came out from the temple which is in heaven, he also having a sharp sickle.
18 And another angel came out from the altar, he that hath power over fire; and he called with a great voice to him that had the sharp sickle, saying, Send forth thy sharp sickle, and gather the clusters of the vine of the earth; for her grapes are fully ripe.
19 And the angel cast his sickle into the earth, and gathered the vintage of the earth, and cast it into the winepress, the great winepress, of the wrath of God.