We have regular base incomes, but DH get a large variable bonus at points throughout the year (and it can range from 0-60% of his ANNUAL income).
I did SAHM for 6 years, and budgeting was interesting. I did a monthly budget averaging the last 3 years' bonuses and dividing that by the number of months I a year. The average of the bonus went into our "luxury" budget items. Our "basic" budget was based on his regular base salary only. When he got a bonus, if it was higher than average, we invested it. If it was lower than average, we reviewed the "luxury" budget items and stopped them for the next year. If he didn't get a bonus, well there were no luxuries! (Actually, he's always gotten some bonus, but we're conservative.)
One year he thought he might get no bonus due to the bad economy, and were worried about layoffs as well. I went back to work part-time. He got a "small" bonus that year anyway and kept his job too! I've continued to work - and we use my salary (after childcare costs) to increase investments and make extra principal payments. Every year I work is 1 year less he has to work for FIRE. :-)
Since it sounds like you could afford the "basic" budget on your salary alone, you could try budgeting that way. Let about 3 months of boyfriend's salary accumulate in an emergency account as a cushion for unusual months. Then going forward, only spend 1/12 of the average of his last 3 year's earnings on "luxury" budget items (this include budgets for saving and investing, but please make sure investments/savings are in a joint account since he isn't your DH yet).