Croatian citizen traveling thru Schengen with non-Croatian spouse

Will the 90/180 Schengen rule apply to us?

No. It does not apply to you because you are a Croatian citizen. As long as you are together, it does not apply to your husband because when he is with you he is a "person enjoying the right of free movement under Union law" for the purposes of the Schengen Borders Code. The definition is found at Article 2(5):

5. ‘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 applies;

The quotation omits point (b), which is not relevant. Your husband falls under the second clause of point (a).

This has the interesting consequence that your husband is not a third-country national for the purposes of the Schengen Borders Code whenever he is traveling with you or to join you. This follows from the next definition, Article 2(6):

6. ‘third-country national’ means any person who is not a Union citizen within the meaning of Article 20(1) TFEU and who is not covered by point 5 of this Article;

Whenever your husband is covered by point 5, that is, when he is traveling with you or to join you, he is therefore not a third-country national.

The Schengen Borders Code applies the 90/180 rule to third-country nationals. It is mentioned in Article 6, "Entry conditions for third-country nationals." Therefore, it does not apply to your husband.

However, the Schengen Borders Code only concerns entry and exit. It doesn't say anything about conditions for remaining on the territory of an EU state. For that, we have to look at the free-movement directive, 2004/38/EC. This lays out several requirements that individual member states must implement in their national law with respect to EU citizens and their family members. ("Family members" is fairly narrowly defined in the directive, but definitely includes spouses.)

The requirements include:

1. Family members traveling with or to join an EU citizen must be admitted with a valid passport (Article 5(1)) unless they pose a threat to "public policy, public security or public health" (Article 27).

2. Family members may be required to have a visa to enter only if the family member is a national of a country whose citizens require a visa for a short visit (Article 5(2)). Because your husband is a US citizen, and US citizens are not required to have visas for short visits, he cannot be required to have a visa.

3. Close family members (including spouses) must be allowed to reside in an EU country "for a period of up to three months without any conditions or any formalities other than the requirement to hold a valid ... passport" (Article 6(2)).

4. Each country may limit the right of residence for more than three months to EU citizens who are workers, self employed, self sufficient, or studying and their family members (Article 7).

5. Family members of EU citizens in the preceding point may be required to register with a deadline of not less than three months. A residence card must be issued in these cases (Articles (8) and (9)).

We will travel to each country in the Europe but will never stay longer than 3 months in each one.

As you can see, there is nothing about the Schengen area in any of this. Your husband, therefore, does not violate the directive as long as you do not remain in any country for longer than three months.