If a non-Catholic family chooses one person to be a godparent, is
his/her spouse automatically considered a godparent as well? Also, is
it considered proper or improper to ask a husband from couple #1 to be
the godfather, and a wife from a different couple, #2, to be the
godmother?

Over the years, I have been asked to be the godmother of four
children; in only one of these cases was my husband the godfather. In
two instances, the godfather was a total stranger to me (though, of
course, he was known well by the child's parents). Generally speaking,
godparents do not have to be married; if they are married, they don't
have to married to each other.

This is so even for Catholics:

"While only one godparent is needed, many people name two persons to
the role. If this is the case, there must be one of each sex (see,
Canon 873). However, they need not be related to one another in any
way. One cannot name more than two godparents."

Roman Catholic Diocese of Wheeling-Charleston
http://www.dwc.org/questions/Faith/godparents3.htm

"The Godparents do not have to be married to each other."

St. Michael's Call
http://www.saint-mike.org/Apologetics/QA/Answers/Faith_Spirituality/f0312150574.html

In the Orthodox faith, the tradition is that godparents are *not*
married to each other:

"Normally Godparents (sponsors) are two Orthodox Christians who are
not brothers and sisters nor married to each other.  This is because a
new spiritual link is formed by their participation in the Holy
Mystery.
  
After the Baptism the Godparents are spiritual family to the one
baptized and to his or her family - and also to each other!  It is
confusing if they are brothers and sisters to begin with. Godparents,
by virtue of their calling, can not marry each other nor may their
children marry each other.  Can you see how confusing it would be if
they were husband and wife to begin with?"

Ukrainian Orthodoxy
http://www.unicorne.org/orthodoxy/articles/answers/baptism.htm 

"One Godparent of the same gender as the child is mandatory, a second
(of the opposite gender) is optional. The two Godparents cannot be
married to each other at the time of the baptism or in the future, as
the spiritual bond of the Godparent with the child being baptized
supercedes any possible bond between the two Godparents."

St. Vladimir Orthodox Church
http://www.stvladimiraami.org/faqs.asp 

Here is a general, nondenominational view of the matter:

"The selection of Godparents is an important task. Different
denominations have various requirements for Godparents, so be sure to
confer with your church before your selection. Typically, the
Godparents are composed of both a female and male member, although not
necessarily from the same couple. However, it is important to note
that only one Godparent is actually required. It is usually the case
that one of the Godparents needs to be a practicing member of the
faith into which the child is being baptized."

What is Christening?
http://www.christening.com/exclusive_article.htm#RESPONSIBILITIES%20OF%20THE%20GODPARENTS

This chart gives a brief description of godparenting in several religions:

Beliefnet: Godparents Across Religions 
http://www.beliefnet.com/features/godparents_chart.html

Google search strategy:

Google Web Search: "godparents" + "married to each other"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=godparents+%22married+to+each+other

Google Web Search: "choosing godparents"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22choosing+godparents

Google Web Search: "requirements" + "godparents"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=requirements+godparents

I hope this helps! Please let me know if anything I've said is unclear
or incomplete.

Best wishes,
pinkfreud

Thanks for all the details. (More than I really need, but I guess
that's what you guys do.)

In my experience (I'm Catholic), although not canonically recognized,
as a courtesy, the (non-godparent) spouse would also be addressed as
"godfather" or "godmother" by the baptizee (in later years, naturally,
as so few can actually speak when baptized(.

Nelson has made a very good point. The spouse of a godparent is often
addressed as "godmother" or "godfather" as a courtesy, even if the
individual does not officially hold that status.