Elliot and Blood have a relationship that can't compare to the others that this boss has. Elliot is completely loyal to Blood and those two are often seen together. The two also seem to have sat next to each other during Blood's tea parties until Alice started coming to them too.
Tweedle Dee & Dum
Blood only sees these two characters really as children, or gatekeepers. They are also very loyal, but have a tendancy to run to the Amusement Park and play when they are supposed to be doing their work... He saves Alice from getting killed by both the twins and Elliot when they first meet.
Blood is the enemy of Gowland. Whenever the two are together, Blood is found making fun of Gowland by calling him by his first name "Mary." The two don't seem to have very successful territory negotiations.
Their relationship is not one of dislike, but neither has much interest in the other. Boris holds some respect for Blood and avoids stepping on his toes, while Blood views Boris as hardly more than a playmate for his gate guards, Dee and Dum.
Being part of the Hatter family Blood is Pierce's boss but they share a mutual dislike over each other. Pierce dislikes Blood because Blood drinks black tea, and Blood dislikes Pierce because the Dormouse drinks black coffee.
Blood seems to be an enemy of Vivaldi when they are in public around people, but they secretly meet with each other in Blood's rose garden as friends. Blood also is Vivaldi's younger brother. They share a love of tea and roses and Alice comments that they both smell as such, one of the things that causes her to make a connection between the two.
Blood dislikes Peter but has no special hatred for him, while Peter hates him more than he does most people. It seems that they hold a grudging respect for one another that doesn't affect their dislikes of each other.
Although Blood will insult Ace at times and even fight him, it is shown in Joker no Kuni no Alice that he is actually wary of Ace, who is one of the two strongest fighters in Wonderland. He knows that Ace doesn't always just wander to the Hatter Mansion on accident, for the Knight has a duty to kill Blood and Elliot. Their interactions are often tense.
Despite Elliot's hatred for Julius, Blood doesn't hate Julius. He dislikes him but mainly considers the Clockmaker a boring and gloomy person, and as such is uninterested in the other. At one point Blood breaks a few clocks hoping that Julius will hand Alice over.
On the surface Blood and Nightmare have a cordial relationship, but in reality Blood is extremely wary of Nightmare. In some media it is suggested that Nightmare knows Blood's secrets.
This doesn't prevent Blood from inviting Nightmare to his tea parties or other social gatherings if the latter is in a relationship with Alice.
Often times, Blood considers Nightmare a nuisance.
They do not have a very good relationship with one another; in Gray's game routes and manga, Blood tends to be one of or the main troublemaker. Blood enjoys provoking the Lizard to alleviate his boredom, even if this means interrupting Gray's work. However, he will never fight with Gray on equal terms because he knows that he will lose, and therefore ensures that he has some advantage (for example, in Omochabako no Kuni no Alice, when Gray was blindfolded).
Blood thinks that since Gray joined Nightmare's faction he's grown soft and boring. He prefers it when Gray is more like his assassin self. He insists that he's providing a service to Gray by giving him an opportunity to stop holding himself back by provoking him into those unfair fights.
Like all of the other role holders, Blood hates Joker.
Their relationship is like Peter and Blood's.
While their face-to-face interactions are civil on the surface, for their personalities prevent them from shouting matches, they are bitter enemies and the bosses of the two biggest mafia in the country. They will work together to defend Alice, but more often than not they prefer not to interact and just let their subordinates fight each other instead.