During a phase transition, what is the nature of the material?

As a material is heated, it increases in temperature until it enters a phase transition. During the transition, added heat does not increase the temperature. As this heat is being added, what is the substance? Is it a mixture of liquid and gas perhaps? If so, what are the proportions?

In other words, what exactly is the substance during one of the flat parts of the temperature vs. heat graph?

http://www.physicstutorials.org/imag...ngeofwater.png