There are four Ancient Greek words for love: agápe, éros, philía (aka phileo), and storgē.
Agape is Godly love. This is the kind of selfless love God wants us to have for other believers and is spelled out in I Corinthians 13. It is the kind of love that strives to put others feelings and needs before your own. It is difficult to find this kind of love in your heart when you list their sins against you. It is easier to find when you focus on the love God has for you in spite of the sins you have done against Him and others. This kind of love requires a sacrifice. This is the kind of love that exists and endures when things are not fun or easy. In humans, it is fallible. We will fail each other in this God-love from time to time, but it should resurface. God's love for us does not fail or waiver because He and His love are perfect.
Phileo (philia) love is the loyal love of friends and family. It is known as the "brotherly" love. It is a strong connection and affection to someone. You can have agape love for your enemies but you can not have phileo love for them. Agape love will endure, but phileo love can be crushed by cruelty. Phileo is where Philadelphia, the city of brotherly love, got its name. Phileo is "love" and adelphos (delphia) means "brother" in the Greek text.
Eros is the Greek word for passionate physical desire and longing for someone. This is the romantic love between couples. The word eros is not mentioned in Scripture, but is where we get the English word erotic from. Eros is the type of love between the man and woman in Song of Solomon.
Storge is a love of acceptance and understanding. I have also heard it described as an genuine caring and loyalty that exists for a difficult person because you comprehend their behavior or struggles. I have a friend that does things she knows she should not do that trouble me to no end, but I care for her and will defend her because I understand what she has been through and what she is seeking. I also have this kind of love for a dog who bites me frequently. She came from an abusive situation and knows nothing better from human hands than what she has seen. I don't like getting bit and dread working with her, but I patiently put up with it because I understand why she bites. When someone talks bad about this dog's behavior, I defend her.
Having love for someone does not mean you put yourself or your family in harm's way. Harm can be physical, mental or emotional. I find it very plausible a husband can have agape love for his wife and still keep himself and his children away from her abusive behaviors. In fact, I know a woman who has agape love for her exhusband. She was lied to, cheated on, stolen from, beaten until she was put into the hospital, etc, etc, etc!!....and still, she asked me to pray for her exhusband's soul. Her love and concern for his well being after all of the abuse she took is something I will never forget. She was well within her rights to end the relationship to prevent more abuse, but she maintains abiding agape love by caring for his well being and salvation.