Microstrip Transmission line characteristics impedance
not all the field lines are bounded between the dielectric material and the microstrip line.

This is true. However, the formula \$C=\frac{\varepsilon_0\varepsilon_R A}{t}\$ applies to the case of quasi-infinite plates. That is, the case where all the field lines are strictly vertical from one plate to the other. This formula neglects fringing fields altogether.
The field lines that &quot;escape&quot; the dielectric into the air are part of the fringing field, not accounted for in the parallel plate capacitance formula. Thus they (and the other fringing fields that are confined to the dielectric) can only add to the capacitance, not subtract from it.