Can a non-EU spouse of EU citizen not resident in EU travel in the EU more than three months?

Yes, you can do that. The freedom of movement rules do not depend on your being resident in Europe.

You should bring a copy of your marriage certificate, preferably legitimized with an apostille. You should be able to find out how to do that from the office that issued the certificate (though I suppose you probably had to do that for the German residence card so you already know how).

This is controlled by Directive 2004/38/EC, the freedom of movement directive, which gives you a right to be in any EU country for up to 3 months without applying for a residence card. Note that the time period is calculated for each country ("member state"), not for the Schengen area as a whole.

Article 6

Right of residence for up to three months

1. Union citizens shall have the right of residence on the territory of another Member State for a period of up to three months without any conditions or any formalities other than the requirement to hold a valid identity card or passport.
2. The provisions of paragraph 1 shall also apply to family members in possession of a valid passport who are not nationals of a Member State, accompanying or joining the Union citizen.

(emphasis added)

To this I can add the experience of my parents, who reside in the United States. My father is an EU citizen; my mother is not. They have on several occasions spent more than three months in France, and the officers once became concerned as my mother presented herself for the exit control. As soon as they realized that she was married to my father, they stamped her out without further discussion.

To avoid that, my parents now present themselves together at the "EU/EEA/CH passports" desk. This is explicitly allowed by the Schengen Borders Code:

First, from Article 2, a definition:

‘persons enjoying the right of free movement under Union law’ means: (a) Union citizens within the meaning of Article 20(1) TFEU, and third-country nationals who are members of the family of a Union citizen exercising his or her right to free movement to whom Directive 2004/38/EC of the European Parliament and of the Council ( 1 ) applies;

Then, from Article 10:

2. Persons enjoying the right of free movement under Union law are entitled to use the lanes indicated by the sign shown in Part A (‘EU, EEA, CH’) of Annex III. They may also use the lanes indicated by the sign shown in Part B1 (‘visa not required’) and Part B2 (‘all passports’) of Annex III.