  Atom interferometers provide a powerful tool for measuring physical constants
and testifying fundamental physics with unprecedented precision. Conventional
atom interferometry focuses on the phase difference between two paths and
utilizes matter waves with fixed coherence. Here, we report on realizing a
Ramsey-Bord\'e interferometer of coherent matter waves dressed by a moving
optical lattice in the gravity direction, and explore the resulting
interference along multiple paths with tunable coherence. We investigate
spatial correlations of atoms both within the lattice and between two arms by
interferometry, and observe the emerging multiple interference peaks owing to
the long-range coherence nature of the Bose-Einstein condensate. Our findings
agree well with theoretical simulations, paving the way for high-precision
interferometry with ultracold atoms.
