Further to earlier answers, the information given so far is bit vague and so might mislead.
The EU spouse has very strong rights to travel freely within the whole of the EU (Schengen is irrelevant to this) with their spouse and children.
These rights include the right for the Third Country national to live indefinitely and work in the member state concerned.
These rights used to be contained in several different laws, but a few years ago the were consolidated. They can be found in 'Directive 2004/38/EC of the European Parliament and of the Council of 29 April 2004 on the right of citizens of the Union and their family members to move and reside freely within the territory of the Member States'
This has to be implemented in an equivalent way in every EU Member State (the Government will be taken to court if it is not).
So if the EU spouse is going to any EU country except the country of their own nationality (but there's even an exception to that exception) and will exercise Treaty Rights (i.e. tourism, looking for a job, taking up a job, living there while being economically self-sufficient) then the non-EU spouse or civil partner has a RIGHT to enter.
Visas are not needed once a Residence Card has been issued to the non-EU national but check the destination state's embassy for any helpful pre-departure procedures as airline staff don't often know the law and this things are changing as Member States revise their procedures.
If a visa is required for entry, it must be issued quickly and under EU law MUST BE FREE OF CHARGE/
The UK procedure for this is called the EEA Family Permit-- see http://en.wikipedia.org/wiki/European_Economic_Area_Family_Permit). Its free of charge, but in my view parts of it are a disproportionate contravention of the requirements of the Directive, and I expect someone may challenge it in the European Court of Justice in the next few years.