Actually, both versions are correct: "Семейное счастие" and "Семейное счастье". "Семейное счастIе" is an example of the old spelling, in the modern spelling we don't use "I" anymore. The phonetic equivalent of it is "Семейное счастие", and this is how Tolstoi called his novel. But the problem is that we don't use the word "счастие" anymore, the modern version is "счастье". So, the modern apaptation of the title is "Семейное счастье".
Russian Language Teacher.