Found one (probably unofficial) way to do it based on the source code of Plots.twin:
let
plt = bar(fill(20, 10), color=:orange, label=false, ylabel="bar plot")
plot!(twinx(plt), randn(10), ylabel="line plot")
plt[1][:yaxis][:mirror] = true
plt[2][:yaxis][:mirror] = false
plt
end