  We present a device demonstrating a lithographically patterned transmon
integrated with a micromachined cavity resonator. Our two-cavity, one-qubit
device is a multilayer microwave integrated quantum circuit (MMIQC), comprising
a basic unit capable of performing circuit-QED (cQED) operations. We describe
the qubit-cavity coupling mechanism of a specialized geometry using an electric
field picture and a circuit model, and finally obtain specific system
parameters using simulations. Fabrication of the MMIQC includes lithography,
etching, and metallic bonding of silicon wafers. Superconducting wafer bonding
is a critical capability that is demonstrated by a micromachined storage cavity
lifetime $34.3~\mathrm{\mu s}$, corresponding to a quality factor of 2 million
at single-photon energies. The transmon coherence times are
$T_1=6.4~\mathrm{\mu s}$, and $T_2^{Echo}= 11.7~\mathrm{\mu s}$. We measure
qubit-cavity dispersive coupling with rate $\chi_{q\mu}/2\pi=-1.17~$MHz,
constituting a Jaynes-Cummings system with an interaction strength
$g/2\pi=49~$MHz. With these parameters we are able to demonstrate cQED
operations in the strong dispersive regime with ease. Finally, we highlight
several improvements and anticipated extensions of the technology to complex
MMIQCs.
