where does matlab distinguish (and then allow me to specify the latter) covariance patterns from covariance structure, aka variance covariance matrix, aka etc.?

i'm new to mixed effects models to begin with, but i'm having an impossible time understanding how to specify nested covariance patterns in fitlme. my current understanding is that with 'CovariancePattern', using fitlme, i'm specifying the covariance pattern between random effects, whereas what i'm trying to specify (or at least view after the function has run) is the variance-covariance matrix/structure(/whatever!) between individual measurements nested inside groups. something like a repeated measures anovan approach might work better, but i'll use whatever works.

my situation: i have very unbalanced data (some groups having as low as 1 measurement, i.e. no repeated measure for that particular group; i need all the data i can get, but i can remove these few singlet groups if necessary). there is one strictly between group factor (genotype) and one mostly between group factor (depth of recording, hi and low); i say "mostly" because i only sampled from both levels of the latter factor in three out of um-teen groups, i.e. most groups are contributing samples to either one level OR the other (e.g. hi OR low) but not both. other than the grouping, there is no dependence between the individual measurements, so i want to constrain the covariances between measurements to be rho within a group (same rho for all groups) and zero otherwise.

i ask because my statistician says that SPSS is handling it, with great facility when he shows me, but i don't even know if i'm using the right nomenclature to translate between these programs...

any help would be appreciated, and i'd be happy to give more details if necessary. thanks, ben