An empirically based analysis of propagation characteristics in two vegetated suburban areas with different types and fractions of vegetation cover in 5G millimeter-wave bands is presented. A basic distance-dependent path loss model with a Gaussian random variance for shadow fading is utilized in accordance with the maximum-power directional and omnidirectional measurement data, therein exploiting significant path loss exponents in the presence of vegetation. In comparison with the existing ITU-R and 3GPP models, the effect of dense-leaved trees on path loss prediction is similar to that of buildings, whereas these standard models are inapplicable for sparse obstacle-line-of-sight (OLoS) links. Consequently, an azimuth-angle-based path loss characterization is proposed considering the antenna pattern, beam misalignment, and blockage effects. Moreover, several composite and cluster-level small-scale channel parameters, such as the number of clusters, delay spread, and angular spread, are extracted. Analysis of the first-arrival cluster in the OLoS setting reveals that forward scattering through foliage is still dominant and is expected to produce a larger azimuth angular spread of the arrival and compact multipath components in the time domain compared with line-of-sight and reflected clusters. Measurement results improve existing 3GPP channel models for suburban macrocell scenarios in millimeter-wave bands.