Baraqiel initially hated Issei due to his misconception about him being an Oppai Dragon and taking advantage of his daughter, taking Azazel's description of him as a "dragon that devours breasts" literally. After the battle against Loki, Baraqiel starts to have a change in view on Issei, even asking him to protect Akeno on his behalf.
In Volume 22, during their fight in the tournament, Baraqiel encouraged Issei to think more about how Akeno feels and what he means to her, reminding him of the time he died which left her in a broken state. Baraqiel was surprised to hear out loud how Issei truly felt for Akeno after he was depressed in thinking Issei chose Rias over his daughter, Akeno and that her happiness would cease, this encouragement pushed Issei to propose to Akeno and promising to make her happy. He came to completely trust in Issei's love for Akeno and broke down crying commenting to his deceased wife, Shuri, that their daughter has found a good man.
Baraqiel loves his daughter very dearly and is fiercely overprotective of her. Baraqiel also held strong guilt and remorse for his failure to protect her mother as he said nothing to rebuke whenever Akeno pointed out his inability to protect Shuri before they reconcile. In Volume 22, he became truly happy for his daughter's happiness in that she has a found a good man in Issei. In Volume 24, he begins helping to organize his daughter's and wedding with Issei, acknowledging her request of wanting to wear a shiromuku for her ceremony and prepares the finest quality for her.
Baraqiel and Azazel have a close friendship. Azazel feels guilty to Baraqiel for making him leave his family which resulted in the death of his wife and strained his relationship with his daughter. Despite this, Baraqiel doesn't bear any grudge against Azazel and still treats Azazel as his good friend.
Baraqiel loved his wife very much. When they first met, Shuri nursed him back to health from the injuries that he sustained from fighting enemy forces. They deepened their relationship and eventually had Akeno. Together, the three of them had a quiet lifestyle until Shuri was tragically killed in her attempt to protect Akeno, claiming that she was an "important and precious daughter of that person". She returns as an apparition in Volume 7, encouraging her daughter to reconcile with Baraqiel, as she knows that he greatly loves and cares for them.