I have a 1.5 centimeter melanoma on the bottom of my foot. How serious is the depth of this?

Thick. Melanomas are considered thin when they are less than 1 mm thick and they are considered thick when they are greater than 4 mm thick. If your melanoma is truly 1.5 cm thick, this would indeed be a very thick melanoma. Check with your doctor to be sure about the depth and that it is not 1.5 mm. A 1.5 cm melanoma would be at high risk for lymph node and distant spread and has a poor prognosis.
Centimeter? I think perhaps you mean millimeter. Melanoma is a potentially danger cancer. Survival would depend on whether your melanoma has traveled to other locations in your body. Have you scheduled your resection and sentinel lymph node biopsy yet?