The main concept of pressure in physics is an absolute quantity, because it gives directly net force on surface from the fluid on one side of it. This force has measurable effects and so absolute value of pressure can be in principle determined.
There is also concept of relative pressure, but used more in engineering/aviation for practical reasons (concept of pressure is used in the context of Earth's atmosphere being the standard value). If the relative pressure of atmosphere in a container has relative pressure -600mbar with respect to standard atmosphere which has absolute pressure 1000mbar, this means the gas in the container has absolute pressure 400mbar. If the balloon is in mechanical equilibrium with this gas, it pushes back on the gas with absolute pressure 400mbar.