Thinking of Catholic School?
Here in Australia we have a third dimension added to the state school/independent school binary: the Catholic school. Originally founded as charitable institutions back in the 19th century, they nowadays inhabit a halfway-house between the public and private spheres: their funding is sourced through a mixture of government tax money and compulsory parental fees.
As a consequence, they usually provide better facilities and extracurricular content than their state counterparts. Yet, like all schools, the quality varies by area and institution. In some areas, such as the well-to-do districts of Sydney, some Catholic schools are essentially well-heeled independent schools in all but name (with fees to match); but across most of the country the average fee sits at roughly $1000 per annum: far cheaper than independent education and not that far from the optional donations the rest of us can pay to state schools, which can amount to $400 in some places.
This means the Catholic school system caters to a sizeable percentage of Australia's pupil intake: about 25%, which puts them proportionally closer to state schools in number of students in the system when compared to independent schools. Parents use them as a kind of 'value added' state school, and funding-wise that's exactly what they are, in a sense.
So what does a Catholic school education give your children, apart from better facilities and more extracurriculars? One of their big strengths is pastoral care, something that is arguably outside the remit of most state schools. The character of the pastoral care varies by institution, but you'd be surprised at the general trend which leans more towards all-round spiritual enrichment as opposed to a purely 'Catholic' education. In fact, the proportion of kids from non-Catholic backgrounds in the Catholic school system is roughly a third, some of which may have other non-Christian faiths, or none at all. Most schools limit the Catholic aspect of their education to a morning prayer and special services on holidays; their RE lessons focus on the universally applicable aspects of the Christian faith, and indeed of other faiths as well.
To sum up: given their nationwide prevalence, relatively modest fees, emphasis on pastoral care and enhanced facilities, Catholic schools present a solid alternative to the state system for children from all backgrounds.