But Griffith has never considered those his family. He's only ever seen them as pawn. He has always longed for a place for himself which he describe as his kingdom and he wants to share the scenery of his dream/his kingdom to the one he saw as his friend. This person is Guts because unlike others, Guts see Griffith as who Griffith truly are, not some high/mighty leader or some smart mastermind. When Griffith showed Guts his dark side (when he asked Guts to kill that noble), Guts just doesn't really care. Guts saw Griffith as Griffith. He didn't have any great image about Griffith unlike any other in the band (those that didn't know the real Griffith and deify him as some ideal/perfect leader). Griffith genuinely believed that he can be himself in the presence of Guts and he feels relaxed, he treasured his companionship with Guts.
The only one he has ever desired in his whole life is Guts. Losing Guts wrecked him completely. This desire grew even greater than his ambition of having a country which explained why he didn't care anymore and sought comfort from the person that is most likely to accept him (beside Guts) which is the princess. Losing Guts is literally losing everything. His world is collapsing. He was realising his country which to him is possible but of all the ones he met his life there is no other than Guts. It shows just how devastated he was when he stop thinking about his dream.
Griffith finally came to term with losing a companion forever when he was locked in the dungeon and tortured for years. Out of all the character, you don't see Griffith showed more emotion to any single person more than Guts. He love Guts. He wanted Guts. He felt betrayed when Guts left him. He felt despair when he was powerless in stopping Guts. He threw all his effort out of the window when Guts left. He felt for Guts too much that the torture and despair turned his love to hatred.
When Guts returned, he was angry, he hated Guts. He blamed Guts for his loss of an able body, of his dream of having a country. Guts has no longer be his greatest desire on a conscious level. This led him to sacrifice everything to achieve his dream again which is the ascension to Godhand. Basically, Griffith was too hurt that he resolved to be extremist.
You know it best that Griffith cared little for Caska. All the time in the eclipse, Femto's eyes were on Guts. He raped Caska to spite Guts. It's his vengeance against Guts. He lost everything so now he want Guts to feel the same too.
When he got a new body, he did say he no longer see Guts as anything significant to him but unconsciously all of his feelings for Guts were still there. They have never gone. In his dream, he dreamed to be with Guts and others.
He was too redeemable and tragic. It was the same as when Lelouch unconsciously ordered Euphemia to massacre the Japanese. It's never because he was evil or because his motive was evil.