You can use the package ucharclasses
to automatically change the font family based on the unicode block in usage. You call it with:
\usepackage[Latin,Cyrillics]{ucharclasses}
\setTransitionsForCyrillics{<at-beginning-of-unicode-block>}{<at-end-of-unicode-block>}
I defined a new russian
environment in order to both set the block language
\newenvironment{russian}
{\begin{otherlanguage*}{russian}
\fontspec{Linux Biolinum O}}
{\end{otherlanguage*}}
and called it with
\setTransitionsForCyrillics{\begin{russian}}{\end{russian}}
biblatex
already automates the language specifications of bibentries based on the hyphenation
field with the babel=hyphen
or the babel=other
package options. In order to have the same functionality in citations, refer to Switching languages for citations according to the bibentry's “hyphenation” field. The MWE below uses the first answer there.
The following MWE uses Linux Biolinum O as the cyrillic typeface, to stress the difference. It is also based on the one proposed in Russian and Japanese and biblatex oh my.
\documentclass{article}
\usepackage{fontspec,microtype}
\defaultfontfeatures{Ligatures=TeX,Scale=MatchLowercase}
\setmainfont{TeX Gyre Pagella}
\usepackage[russian,english]{babel}
\usepackage[babel=other,backend=biber,style=verbose-trad3]{biblatex}
\usepackage[Latin,Cyrillics]{ucharclasses}
\newenvironment{russian}
{\begin{otherlanguage*}{russian}
\fontspec{Linux Biolinum O}}
{\end{otherlanguage*}}
\setTransitionsForCyrillics{\begin{russian}}{\end{russian}}
\makeatletter
\AtEveryCitekey{%
\blx@langsetup\abx@field@hyphenation%
\blx@hyphenreset%
}
\makeatother
\begin{filecontents}{\jobname.bib}
@article{Dubrovin1906,
author = { Дубровин, А. И },
title = { Открытое письмо Председателя Главного Совета Союза Русского Народа А. И. Дубровина от 2 декабря 1906 года митрополиту Санкт-Петербургскому Антонию, Первенствующему члену Священного Синода },
journal = { Вече },
edition = { 97 },
year = { 1906 },
month = { 7 дек. 1906 },
pages = { 1-3 },
keywords = {primary},
hyphenation = { russian },
language = { russian }
}
@article{Brumbaugh1947,
author = { Brumbaugh, Thoburn T },
title = { The Protestant Handicap in Japan. },
journal = { Christian Century },
volume = 64,
edition = 23,
year = { 1947 },
month = { 4 June 1947 },
pages = { 708-709 },
keywords = {primary},
hyphenation = { english },
language = { english }
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\textcite{Brumbaugh1947}
\autocite{Brumbaugh1947}
\textcite{Dubrovin1906}
\autocite{Dubrovin1906}
\printbibliography
\end{document}

ucharclasses
package. (See also Switching languages for citations according to the bibentry's “hyphenation” field)