  We formulate a property strengthening the Disjoint Amalgamation Property and
prove that every Fraisse structure in a finite relational language with
relation symbols of arity at most two having this property has finite big
Ramsey degrees which have a simple characterization. It follows that any such
Fraisse structure admits a big Ramsey structure. Furthermore, we prove
indivisibility for every Fraisse structure in an arbitrary finite relational
language satisfying this property. This work offers a streamlined and unifying
approach to Ramsey theory on some seemingly disparate classes of Fraisse
structures. Novelties include a new formulation of coding trees in terms of
1-types over initial segments of the Fraisse structure, and a direct
characterization of the degrees without appeal to the standard method of
"envelopes".
