Wiki calls them Dome-Switch or Chiclet keyboards:
Dome-switch keyboards are a hybrid of flat-panel membrane and mechanical-switch keyboards. They bring two circuit board traces together under a rubber or silicone keypad using either metal "dome" switches or polyurethane formed domes. The metal dome switches are formed pieces of stainless steel that, when compressed, give the user a crisp, positive tactile feedback. These metal types of dome switches are very common, are usually reliable to over 5 million cycles, and can be plated in either nickel, silver or gold. The rubber dome switches, most commonly referred to as polydomes, are formed polyurethane domes where the inside bubble is coated in graphite. While polydomes are typically cheaper than metal domes, they lack the crisp snap of the metal domes, and usually have a lower life specification. Polydomes are considered very quiet, but purists tend to find them "mushy" because the collapsing dome does not provide as much positive response as metal domes. For either metal or polydomes, when a key is pressed, it collapses the dome, which connects the two circuit traces and completes the connection to enter the character. The pattern on the PC board is often gold-plated.
Both are common switch technologies used in mass market keyboards today. This type of switch technology happens to be most commonly used in handheld controllers, mobile phones, automotive, consumer electronics and medical devices. Dome-switch keyboards are also called direct-switch keyboards.
Keep in mind that instead of custom poly domes or metal domes, you could use the rubber part over mechanical switches.