I’m currently discerning a call to the priesthood and I was wondering if there are any religious orders where the male & female branches work together often.
In our parish, we have priests and nuns. The nuns are teachers at the parish school. The pastoral vicar is the priest for the school (celebrates mass for the children every day, etc.) So he works with the nuns on a daily basis. The nuns also work the the male teachers in the school, the altar servers, etc. I don’t know if this is what you meant, but it’s what I thought of when I saw your question because our younger priest often refers to different projects he is working on with the nuns (who are also young).
The order that Fr. Andrew Apostoli belongs to, the Franciscan Friars of the Renewal, have a link on their website to the Franciscan Sisters of the Renewal, and I know they do some work together in New York. I am not sure how they are affiliated. Their habits are very similar.
Note that there is a picture of both the friars and sisters together.
The Franciscans (Minor Conventuals) and Franciscan Sisters in my town have a number of joint ministries. Missionaries like the Maryknollers work together, too… And so do Vincentians and Daughters of Charity. A number of Benedictine communities of men and women also work closely together. I think you just need to look at various communities. Certainly a lot of them are open to working together, particularly those with common founders and so on.
Institute of the Incarnate Word & Servants of the Lord and the virgin of Matara.
There’s the Benedictines. Although they don’t live together often their monasteries are geographically close. The abbey I’m associated with is about 120 km from a women’s abbey of the same congregation (Solesmes). Our abbey provides the chaplains to celebrate the Eucharist at the women’s abbey. In Europe, often the men’s and women’s abbeys are within sight of each other.
The Monastic Fraternity of Jerusalem is a young monastic institute of diocesan right, that admits men and women. They live in separate quarters on the same property (and independently from one another) but come together to celebrate the liturgy. They are based in France and have a community in Montreal. Their liturgy has heavy oriental/byzantine elements, and is sung by the women and men in polyphony. Their monasteries are in the heart of the cities in which they reside, they are called to witness to monasticism in the heart of urban life. They are heavily involved in adoration and took over the Sanctuary of the Blessed Sacrament in Montreal, which they now administer after the community that administered it before were forced to give it up due to lack of vocations.
The Monastic Fraternity is a young community which might appeal to someone younger aspirants. However, it lives in French!
In general, most apostolic communities with male and female branches often work together. However, I doubt there’s a community that always does as often one branch or the other will get bigger and establish houses where the other branch is not - for example, I’m a priest with the Legionaries of Christ and in general we work closely with consecrated laywomen in Regnum Christi but it just happens the city I’m in doesn’t have a house of theirs - so I don’t.
Monastic, or semi-monastic orders rarely do.