It depends on the number of families.


Let $X$ be the number of children in a family, it is geometric random variable with $p=0.5$, i.e.,
$$
P(X = x) = 0.5^x, x=1,2,3...
$$
which implies $E(X) = 2$

Suppose there are $N$ families in the country, the girl ratio is
$$
 \frac{N}{ \sum X_i}
$$

Since $\sum X_i /N \rightarrow E(X) = 2$ (law of large number), the ratio coverages to 1/2 if $N \rightarrow \infty$.


If there are only finite families, let $T$ be the total number of children of the country: $T = \sum X_i$, then $T$ has a negative binomial distribution with pmf
$$
P(T=t) = C^{t-1}_{N-1}  0.5^t, t = N, N+1...
$$

It implies
$$
E\left[ \frac{N}{\sum X_i} \right] = E\left[ \frac{N}{T} \right]  = \sum_{t=N}^{\infty} \frac{N}{t} C^{t-1}_{N-1} 0.5^t  = {_2F_1} (N, 1, N+1, -1)
$$
where $_2F_1$ is the hypergeometric function.

Therefore the expected girl ratio is ${_2F_1} (N, 1, N+1, -1) $.