Such a city would need to built with a significant portion on water. This could be done like Venice, as Tim B has said, or it could be done in a way like described as in this question. This question asks about how a completely floating city could be created. The question focuses on engineering hurtles, but I liked the idea. For this answer I will be focusing on the second method.
If the whole town was built entirely on water, mer-people would likely have houses built on the underside or side of the city platform. Likely more expensive houses would built on the side, with the cheapest houses being in the center, because the houses on the edge would get more sunlight. If part of the city were submerged, the same would be largely true, with the buildings stuck to the outside of the city for the mer-people.
On the bottom of the floating city their would be stairways that opened up into the ocean. These stairways would go down a little ways into the water, allowing mer-people to get a handle on them before leaving the water. Humans would also have a place to push off if they ever visited the mer-folk. I expect humans in this kind of city would be significantly better at swimming, because their neighbors would live underwater.
The city could also be merely built on the edge of the sea as well, possibly coming closer to the ocean than a normal city would. The merfolk's houses would be in the sea, while the human's homes would be on land. The beach between would be a common place, like a large park. The key to having this land-sea city work would be a special system of sidewalks. Along side the sidewalks would be a series of slides (made out of metal or a slippery plastic), and large water-filled tubes. Mer-people could slide down the slides (occasionally pushing themselves along with their arms), and swim up the tubes. This would allow merfolk to travel around in the city. The tubes would be more effective if they were filled with water, like a water slide, but this would be expensive and prevent two way travel on flat ground.
Likely there would be a public transport system, either from the government or used commercially, that would take merfolk and people to and from the beach, as each group would likely only own motorized transport in their own "home" area.
Socially there would likely be tension between the merfolk and the humans, like we have racial tension now. It is likely that the city would be ruled by a joint council of mer-people and humans. Laws would have to be made to protect both groups from the other, and officials would need to be watched for corruption.
Technologically the humans would probably have a higher focus on the water than we do now. More energy would be put into make humans be able to easily breathe/live in the water. Scientists might also focus on make the mer-people's transition to land easier too, though as the merfolk have lungs, this isn't as much of a problem.